A square and an equilateral triangle have equal perimeters. The area of the triangle is 8 sqrt 3 square inches. What is the number of inches in the length of the diagonal of the square?

find side length of triangle

1/2 b h = 8 sqrt3

bh = 16 sqrt3

b * b sin60 = 16 sqrt3

b^2 sqrt3/2 = 16 sqrt 3

b^2 = 32

b = sqrt 32

so perimeter is 3 sqrt 32 square side is then 3/4 sqrt 32

diagonal^2 is 2 (3/4 sqrt32)^2 = 18/16 *32 d = 6 in