# Thread: [SOLVED] Exact value of a Square's diagonal

1. ## [SOLVED] Exact value of a Square's diagonal

This was a question on a Math test that I got wrong, I'm guessing because I didn't do proper exact value:

If the area of a square is 121 square inches, what is the exact value of one of the diagonals?

I used square roots to find length and width (11 inches), and Pythagorean theorem to find the diagonal (15.55634919 inches) but then forgot how to use exact value.

Can someone tell me if my previous math was correct, and then show me how to put the diagonals into exact value?

2. Is $d$ is diagnol then $d^2 = 11^2 + 11^2 = 2\cdot 11^2\implies d = 11\sqrt{2}$.

3. Originally Posted by Blodwynne
This was a question on a Math test that I got wrong, I'm guessing because I didn't do proper exact value:

If the area of a square is 121 square inches, what is the exact value of one of the diagonals?

I used square roots to find length and width (11 inches), and Pythagorean theorem to find the diagonal (15.55634919 inches) but then forgot how to use exact value.

Can someone tell me if my previous math was correct, and then show me how to put the diagonals into exact value?

The side length is indeed 11 and by the Pythagorean theorem you would get...

$11^2+11^2=c^2$

collecting like terms we get

$2 \cdot 11^2=c^2$

Taking the square root

$\sqrt{2 \cdot 11^2}= \sqrt{c^2}$

simplifying

$\sqrt{2}\cdot \sqrt{11^2}=c$

$11 \sqrt{2}=c$
Is $d$ is diagnol then $d^2 = 11^2 + 11^2 = 2\cdot 11^2\implies d = 11\sqrt{2}$.