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

Question

anonymous · Answer

|dw:1371618091206:dw|

whpalmer4 · Answer

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

whpalmer4 · Answer

sorry, that should end with 
$$2s^2=64$$$$s=$$

anonymous · Answer

would the answer be 8?

whpalmer4 · Answer

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
$$s=\sqrt{2*2*2*2*2} = \sqrt{(2*2)*(2*2)*2} $$$$= \sqrt{2*2}*\sqrt{2*2}*\sqrt{2} = 2*2*\sqrt{2}=4\sqrt{2}$$

anonymous · Answer

thank you man that makes perfect sense!

whpalmer4 · Answer

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