Question

What is the length of side s of the square shown below?

Answer 1

use the Pythagorean theorem. both sides are length s, the hypotenuse is 8, so \[s^2+s^2=8^2\]\[2s^2=64\[s=\}

Answer 2

sorry, that should end with
\[2s^2=64\]\[s=\]

Answer 3

would the answer be 8?

Answer 4

Nope. if the equation was \[s^2=64\]then 8 would be the answer, because 8*8 = 64.
However, your equation is \[2s^2=64\]and 2*8*8=128, not 64.

If you divide both sides by 2, you get\[s^2=32\]We can factor 32 into 32=2*2*2*2*2=2^5
\[s=\sqrt{2*2*2*2*2} = \sqrt{(2*2)*(2*2)*2} \]\[= \sqrt{2*2}*\sqrt{2*2}*\sqrt{2} = 2*2*\sqrt{2}=4\sqrt{2}\]

Answer 5

thank you man that makes perfect sense!

Answer 6

if you have a 45/45/90 triangle, the hypotenuse is always \(\sqrt{2}\) * the length of the side