SOLUTION: A square and an equilateral triangle have equal perimeters. The area of the triangle is 8 square root of 3 sq. in. Determine the length of the diagonal of the square.

Question 1073507: A square and an equilateral triangle have equal perimeters. The area of the triangle is 8 square root of 3 sq. in. Determine the length of the diagonal of the square.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
One side of the equilateral triangle, 2x.
Area, .
Area of the triangle given,

, one whole side of the equilateral triangle.
Perimeter of both figures: .

One side of the square of same perimeter is one quarter of that:
side of square, .

Diagonal of the square:

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