How to Find the Measurement of the Diagonal Inside a Rectangle

Step-by-Step Guide

1. 1

   Step 1: Set up the formula for the Pythagorean Theorem.

   The formula is a2+b2=c2{\displaystyle a^{2}+b^{2}=c^{2}}, where a{\displaystyle a} and b{\displaystyle b} equal the side lengths of a right triangle, and c{\displaystyle c} equals the length of a right triangle’s hypotenuse.You use the Pythagorean Theorem because a diagonal of a rectangle cuts the rectangle into two congruent right triangles.The length and width of the rectangle are the side lengths of the triangle; the diagonal is the hypotenuse of the triangle.
2. 2

   Step 2: Plug the length and the width into the formula.

   These should be given, or you should be able to measure them.
   
   Make sure you are substituting for a{\displaystyle a} and b{\displaystyle b}.
   
   For example, if the width of a rectangle is 3 cm, and the length is 4 cm, your formula will look like this: 32+42=c2{\displaystyle 3^{2}+4^{2}=c^{2}}. , Remember, squaring a number means to multiply the number by itself.
   
   For example:32+42=c2{\displaystyle 3^{2}+4^{2}=c^{2}}9+16=c2{\displaystyle 9+16=c^{2}}25=c2{\displaystyle 25=c^{2}} , The easiest way to find a square root is to use a calculator.
   
   You can use an online calculator if you do not have a scientific calculator.This will give you the value of c{\displaystyle c}, which is the hypotenuse of the triangle, and the diagonal of the rectangle.
   
   For example:25=c2{\displaystyle 25=c^{2}}25=c2{\displaystyle {\sqrt {25}}={\sqrt {c^{2}}}}5=c{\displaystyle 5=c}So, the diagonal of a rectangle with a width of 3 cm and a length of 4 cm is 5 cm.
3. 3

   Step 3: Square the length and width

4. 4

   Step 4: then add these numbers together.

5. 5

   Step 5: Take the square root of each side of the equation.

Detailed Guide

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