How do you find the side length of a square if you are just given the diagonal length?

The diagonal of a square creates a 45-45-90 triangle within the square..

This special right triangle can be used to find the side length.

Transcript

"Let's look at a square Think about a square. Earlier in the unit we talked about the diagonal of a square. You have a square with a diagonal of 10 centimeters. What is the length of each side? Let's mark our angles. We have 90 degrees angles, because it is a square, and we know that a square the diagonal bisects the angle so it is a 45-45-90 triangle. Let's pull this triangle out. If this side is 10, which is the diagonal, this angle will be 90 degrees, and these two are 45 degrees. Remember the rules, the rules for a 45-45-90 = x, x x√2, two sides are the same so it is a x√2 problem. Let's take 10 is equal to √2 (10=√ 2)and solve for x. Divide both sides by √ 2 because you are getting smaller, you are getting the hypotenuse. Next I need to rationalize that so I'm dividing 10 by √ 2, and I have to clear the radical out, so multiply by √ 2/√ 2 , and I get 2 on the bottom, and 10√ 2, and simplify that to 5√ 2 So each side is going to have a length of 5√ 2. That is how you find the length of each side of a square from the diagonal length of a square. Each side will measure 5√ 2. That is how you find the length of each side given the diagonal. Inside a square you have a 45-45-90 right triangle."

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