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.

Algebra ->  Equations -> 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.      Log On


   

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(39616) About Me  (Show Source):
You can put this solution on YOUR website!
One side of the equilateral triangle, 2x.
Area, x%5E2%2Asqrt%283%29.
Area of the triangle given, 8sqrt%283%29=x%5E2%2Asqrt%283%29

x=2sqrt%282%29

2x=4sqrt%282%29, one whole side of the equilateral triangle.
Perimeter of both figures: 12sqrt%282%29.


One side of the square of same perimeter is one quarter of that:
side of square, 3sqrt%282%29.

Diagonal of the square:
sqrt%28%289%2A2%29%5E2%2B%289%2A2%29%5E2%29
sqrt%2818%2B18%29
sqrt%2836%29
highlight%28diagonal=6%29