[SOLVED] Exact value of a Square's diagonal

**Blodwynne** · March 9th 2008, 05:03 PM

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?

**ThePerfectHacker** · March 9th 2008, 05:07 PM

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

**TheEmptySet** · March 9th 2008, 05:08 PM

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

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

moving things about and simplifying

$11 \sqrt{2}=c$

**Blodwynne** · March 9th 2008, 05:11 PM

Originally Posted by ThePerfectHacker

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

I'm going to go bash my head against the desk, because that should have been ridiculously obvious to me. Same thing happened with and earlier problem as well. *shakes head*.

Thanks a lot.

~Wynne

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