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
