SOLUTION: A square and an equilateral have equal perimeter. If the area of the triangle is 9 sqrt(3) cm squared, find the exact length of the diagonal of the square.

Question 1121142: A square and an equilateral have equal perimeter. If the area of the triangle is 9 sqrt(3) cm squared, find the exact length of the diagonal of the square.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
This can be only a way to get started, if you want:
Let 2x be the side length of the equilateral triangle.
Let y be the altitude or height of the equilateral triangle.

and therefore side of equilateral triangle .

You continue from here...
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Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The area of an equilateral triangle with side length s is .

Give that the area of the triangle is 9*sqrt(3), the side length is 6:
--> --> s = 6.

Now find the perimeter of the triangle, which is the same as the perimeter of the square; so you can find the length of a side of the square and then find the length of the diagonal.
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