How To Find Diagonal Length Of A Rectangle

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A diagonal is a straight line that connects one corner of a rectangle to the contrary corner.^[one] A rectangle has two diagonals, and each is the same length.^[ii] If you know side lengths of the rectangle, y'all can easily discover the length of the diagonal using the Pythagorean Theorem, since a diagonal divides a rectangle into two right triangles. If you don't know the side lengths, but y'all have other information, such equally the expanse and perimeter, or the relationship between side lengths, some extra steps will allow you to find the length and width of the rectangle, and from at that place you tin can use the Pythagorean Theorem to discover the length and width of the diagonal.

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3. iii

   Foursquare the length and width, and then add these numbers together. Remember, squaring a number means to multiply the number by itself.

4. 4

   Take the square root of each side of the equation. The easiest way to notice a square root is to use a computer. You lot tin can use an online calculator if you do non have a scientific calculator.^[five] This will give you the value of ${\displaystyle c}$ , which is the hypotenuse of the triangle, and the diagonal of the rectangle.

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1. ane

   Set the formula for the surface area of a rectangle. The formula is ${\displaystyle A=lw}$ , where ${\displaystyle A}$ equals the area of the rectangle, ${\displaystyle l}$ equals the length of the rectangle, and ${\displaystyle due west}$ equals the width of the rectangle.^[6]

2. ii

   Plug the expanse of the rectangle into the formula. Make sure you substitute for the variable ${\displaystyle A}$ .

   • For case, if the area of the rectangle is 35 square centimeters, your formula volition look similar this: ${\displaystyle 35=lw}$ .

3. 3

   Rearrange the formula, finding a value for $$ due west {\displaystyle w} . To exercise this, separate both sides of the equation by ${\displaystyle l}$ . Prepare this value aside. You will plug it into the perimeter formula later.

4. 4

   Fix the formula for the perimeter of a rectangle. The formula is ${\displaystyle P=2(due west+50)}$ , where ${\displaystyle due west}$ equals the width of the rectangle, and ${\displaystyle 50}$ equals the length of the rectangle.^[7]

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   Plug the value of the perimeter into the formula. Make certain yous substitute for the variable ${\displaystyle P}$ .

   • For example, if the perimeter of a rectangle is 24 centimeters, your formula will look like this: ${\displaystyle 24=two(w+l)}$ .

6. 6

   Divide both sides of the equation by ii. This will requite y'all the value of ${\displaystyle westward+50}$ .

7. 7

   Plug the value of $$ west {\displaystyle westward} into the equation. Use the value y'all institute by rearranging the formula for area.

8. 8

   Cancel out the fraction in the equation. To do this, multiply both sides of the equation by ${\displaystyle l}$ .

9. 9

   Ready the equation to 0. To practise this, subtract the first-degree term from both sides of the equation.

10. 10

    Reorder the equation past order of terms. This ways the term with the exponent volition be first, followed by the term with the variable, followed past the constant. When reordering, make sure you keep the appropriate positive and negative signs. You lot should annotation that the equation is now set as a quadratic equation.

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12. 12

    Find the values of $$ l {\displaystyle 50} . To do this, gear up each term to zero and solve for the variable. You will find two solutions, or roots, to the equation. Since you lot are working with a rectangle, the two roots will exist the width and length of your rectangle.

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14. xiv

    Plug the width and length into the formula. It doesn't matter which value you lot employ for which variable.

    • For example, if you found the width and length of the rectangle are five cm and 7 cm, your formula will await like this: ${\displaystyle 5^{ii}+vii^{2}=c^{2}}$ .

15. 15

    Square the width and length, and then add these numbers together. Remember, squaring a number means to multiply the number past itself.

16. 16

    Have the square root of each side of the equation. The easiest way to find a square root is to use a calculator. Yous can use an online calculator if you do non take a scientific estimator.^[ten] This will requite you the value of ${\displaystyle c}$ , which is the hypotenuse of the triangle, and the diagonal of the rectangle.

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1. 1

   Write a formula explaining the relationship between the side lengths. ^[11] Y'all can isolate the length ( ${\displaystyle l}$ ) or the width ( ${\displaystyle w}$ ). Set this formula aside. You will plug it into the area formula later.

2. ii

3. 3

   Plug the expanse of the rectangle into the formula. Brand sure you substitute for the variable ${\displaystyle A}$ .

   • For example, if the area of the rectangle is 35 foursquare centimeters, your formula will look like this: ${\displaystyle 35=lw}$ .

4. iv

   Plug the relational formula for the length (or width) into the formula. Since y'all are working with a rectangle, it doesn't thing whether y'all work with the ${\displaystyle l}$ or ${\displaystyle w}$ variable.

5. 5

   Fix upwardly a quadratic equation. To do this, use the distributive property to multiply the terms in parentheses, then set the equation to 0.

6. half dozen

7. 7

   Discover the values of $$ l {\displaystyle l} . To do this, ready each term to zilch and solve for the variable. You will find two solutions, or roots, to the equation.

8. eight

   Plug the value of the length (or width) into your relationship formula. This will give yous the length of the other side of the rectangle.

9. 9

10. 10

    Plug the width and length into the formula. It doesn't matter which value you use for which variable.

    • For example, if you lot found the width and length of the rectangle are 5 cm and 7 cm, your formula will look like this: ${\displaystyle 5^{ii}+vii^{ii}=c^{two}}$ .

11. 11

    Square the width and length, then add these numbers together. Remember, squaring a number means to multiply the number by itself.

12. 12

    Take the square root of each side of the equation. The easiest mode to find a square root is to use a reckoner. Yous tin can use an online calculator if you do not take a scientific calculator.^[16] This will give you the value of ${\displaystyle c}$ , which is the hypotenuse of the triangle, and the diagonal of the rectangle.

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Add New Question

• Question

  The diagonal of a rectangle is 25 cm. If one of the rectangle'southward sides is 15 cm, how do I calculate the area?

  

  Use the Pythagorean Theorem to find the other side. Then multiply the length by the width.

• Question

  What is the diagonal if the width is 24' and the length is xx'?

  

  LyKaxandra Caimoy

  Customs Answer

  √[(24^2 )+(20^2)] = √576+400 = √976 = four√61`

• Question

  What is the diagonal measurement of a rectangle 150 feet in length by 100 feet in width?

  

  Utilize the Pythagorean Theorem (a^2 + b^2 = c^2). A and B are the lengths of the two sides of the rectangle. To get the length of the hypotenuse, you would need to solve for C. C is the square root of (A squared plus B squared). So c = (a^2 + b^2)^.5.

• Question

  A rectangular carpeting has an area 120 square meters and a perimeter of 46 meters. How do I find its diagonal?

  

  The length plus the width equals half the perimeter (23). Let ten equal the width. So (23 - x) is the length. Therefore, (x)(23 - x) = 120 (the area). Solve for x: (x)(23 - x) = 23x - x² = 120. And so 23x - x² - 120 = 0. Rewrite the equation slightly and multiply both sides past (-i): x² - 23x + 120 = 0. Factor the left side: (x - 8)(10 - 15) = 0. 10 = eight or fifteen. That ways that the width of the rectangle is either 8 or 15, and the length is the other number. So the width is 8 cm, and the length is fifteen cm (because the length is defined equally the longer dimension). Use the Pythagorean theorem to find the diagonal: viii² + 15² = the square of the diagonal (d). So 64 + 225 = 289 = d², and d = 17 cm.

• Question

  How can I find the area of a rectangle if I but know its perimeter and diagonal?

  

  Considering yous cannot find the length and width of a rectangle if all you know is the perimeter and the diagonal, you cannot calculate the surface area.

• Question

  How do I find a foursquare root?

  

  Most calculators take a square root button. You lot can also estimate the value manually if you are familiar with perfect squares. For case, if you lot wanted to know the foursquare root of 10, you would expect it to be betwixt 3 and 4 since 10 is between 9 and 16 (the squares of three and 4, respectively). Yous would also expect the square root to exist closer to 3 than 4, since 10 is much closer to ix than to 16. (The respond is 3.16.)

• Question

  What are the three points of contact for a ladder?

  

  Betwixt two hands and two feet, you have four potential contact points. To accept three contact points, means you either demand to accept two feet and one hand or 2 easily and one foot in contact with the ladder at all times. If you are shifting from two feet and ane mitt in contact to i pes and two hands in contact (or vice versa), you should always return to the ii anxiety and two hands position first.

• Question

  What is the diagonal measurement for an expanse of 15.one past xiii.0?

  

  If the length and width of a rectangle are 15.1 by 13.0, and so you lot can use the pythagorean theorem to calculate the length of the diagonal since it forms a right triangle. The pythagorean formula is a^two + b^2 = c^two." Let a=xv.1 and b=xiii. 15.1 squared equals 228.01; 13 squared equals 169; add them together for 397.01. Now we know that c squared must equal 397.01. To solve for c, nosotros take the square root of 397.01, which is 19.925. This reply makes sense because it is longer than both the length and the width.

• Question

  How can I find the length of a rectangle by using the diagonal?

  

  LyKaxandra Caimoy

  Community Answer

  At least i of the side of the rectangle must be given to easily solve the length. Yous will just simply square the length given and subtract information technology to the square of the diagonal. And then, go the square root of the departure. The reply would be the width (or the opposite side) of the rectangle.

• Question

  Can I work out the length and width combinations if I know the diagonal?

  

  If the rectangle is a foursquare, then yes. If the rectangle is non a square, then unfortunately no. If the rectangle is a square, and so you can square the diagonal and divide by two to detect the expanse of the foursquare. Then, by square rooting that value, you find the value of the side length.

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Commodity Summary X

To find a measurement of a diagonal within a rectangle, showtime by finding the rectangle's width and length. Next, square the width and length and add them together. For example, if your rectangle is three cm wide and four cm long, square these numbers to get nine and 16. Add them to go 25, then find the square root of 25 to become five. Therefore, the measurement of the diagonal for your rectangle is 5 cm. To learn more, including how to use area and perimeter to notice the measurement of a diagonal, scroll downwards.

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