SOLUTION: If the area of a square is 169 cm2, what is the length of the diagonal?

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Question 230563: If the area of a square is 169 cm2, what is the length of the diagonal?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
If the area of a square is 169 cm2, what is the length of the diagonal?

Step 1. The area of a square with side A=s%5E2=169 square cm.

Step 2. Take the square root to get s=sqrt%28169%29=13 cm.

Step 3. The diagonal splits the square into two right triangles. As a result, we can use the Pythagorean Theorem which says that the sum of the square of the legs is equal to the hypotenuse. The legs are the sides of the square given as s and let d be the diagonal. Then,

d%5E2=s%5E2%2Bs%5E2

d%5E2=2s%5E2

Take the square root to both sides of the equation

sqrt%28d%5E2%29=sqrt%282s%5E2%29

d=s%2Asqrt%282%29

d=13%2Asqrt%282%29

d=18.38

Step 4. ANSWER: The diagonal d=13%2Asqrt%282%29 cm or d=18.38 cm

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J