SOLUTION: A square has an area of 81 square centimeters. what is the length of a diagonal of the square?

Question 805883: A square has an area of 81 square centimeters. what is the length of a diagonal of the square?
Answer by trx1150(14) (Show Source): You can put this solution on YOUR website!
🔲 I will do by best to explain this problem since I can't exactly insert a labeled picture of a square. For reference, you can look at the tiny square I put in the top left :-)

So we know that the square's area is 81, and using the formula A=length*width, we also know that each side of the square is 9 centimeters. Picture the diagonal of the square running from the top left to the bottom right. This now cuts the square into two triangles, but we only need to look at one triangle to solve the problem.

The two legs of the triangle on the left and bottom are each 9 centimeters. We need to solve for the diagonal of the square, or the hypotenuse of the traingle. By using the pythagorean theorem, we know that . a and b are both 9, so we can plug those both into the formula to solve for what we're looking for: c.

We now know that the hypotenuse of the triangle, which is also the diagonal of the square, is . This can be further simplified to .

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