SOLUTION: A circle inside a square just touches its sides. If the area of the circle is 341.9 cm^2, what is the length of a side of the square?

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Question 1031229: A circle inside a square just touches its sides. If the area of the circle is 341.9 cm^2, what is the length of a side of the square?

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The key to understanding the solution is recognize that a diagonal of the square is a diameter of the circle.

pi%2Ar%5E2=A, and you know A.

Letting d be diameter,
pi%2A%28d%2F2%29%5E2=A
highlight_green%28d%5E2=4A%2Fpi%29
d=2sqrt%28A%2Fpi%29

Another key to solving is recognize the square is two 45-45-90 special right triangles, and you can use Pythagorean Theorem formula.
Let x be a side of the square.
2x%5E2=d%5E2
and you can solve this for x.

This solution almost but not finished, was done purely in symbols, and you can finish.