SOLUTION: Find the length of the diagonal of a cube with side length 10cm. Thank you.

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Question 457307: Find the length of the diagonal of a cube with side length 10cm.
Thank you.
Found 2 solutions by poliphob3.14, nerdybill:
Answer by poliphob3.14(115) About Me  (Show Source):
You can put this solution on YOUR website!
First using Pythagorean Theorem we find the diagonal of one side:
10%5E2%2B10%5E2=x%5E2=>x=10sqrt%282%29cm. Using again the Pythagorean Theorem
we find the diagonal of the cube:d%5E2=%2810sqrt%282%29%29%5E2%2B10%5E2=>d%5E2=sqrt%28300%29
=>d=10sqrt%283%29cm.
Answer:The diagonal of the cube is 10sqrt%283%29cm.

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Find the length of the diagonal of a cube with side length 10cm.
First, find diagonal of base:
let d = diagonal of base
then
d^2 = 10^2 + 10^2
d^2 = 100 + 100
d^2 = 200
d = sqrt(200)
.
Now, find diagonal of cube
let x = diagonal of cube
x^2 = [sqrt(200)]^2 + 10^2
x^2 = 200 + 100
x^2 = 300
x = sqrt(300)
x = sqrt(3*10*10)
x = 10*sqrt(3)
x = 17.32 cm