SOLUTION: a cubic iron grid has side length 10m. find the length of the diagonal brace of the cube

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Question 693724: a cubic iron grid has side length 10m. find the length of the diagonal brace of the cube
Answer by MathLover1(20849) About Me  (Show Source):
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given:
side length a=10m

use Pythagorean theorem to find first the length of shorter diagonal AE=d%5B1%5D:
d%5B1%5D%5E2=a%5E2%2Ba%5E2
d%5B1%5D%5E2=10%5E2%2B10%5E2
d%5B1%5D%5E2=100%2B100
d%5B1%5D%5E2=200
d%5B1%5D=sqrt%28200%29
highlight%28d%5B1%5D=14.14%29
now we can find longer diagonal (AF=d) as a hypotenuse of a right-angle triangle AEF
d%5E2=d%5B1%5D%5E2%2Ba%5E2
d%5E2=%2814.14%29%5E2%2B10%5E2
d%5E2=200%2B100
d%5E2=300
d=sqrt%28300%29
highlight%28d=17.32%29