Asquare and an equilateral triangle have equal perimeters. the area of the triangle is $2\sqrt {3}$ square inches. what is the number of inches in the length of the diagonal of the square?

An equilateral triangle with side length has area , so that

Then the triangle, and hence the square, has a perimeter of .

The perimeter of a square with side length is , so that

The length of the diagonal of any square is longer than the length of its side, so that this square's diagonal length is

x=30

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