The perimeter of an equilateral triangle is inches more than the perimeter of a​ square, and the side of the triangle is inches longer than the side of the square. Find the side of the triangle.

Question

The perimeter of an equilateral triangle is

4

inches more than the perimeter of a​ square, and the side of the triangle is

4

inches longer than the side of the square. Find the side of the triangle.

Answer 1

For the equilateral triangle, all 3 sides are equal (length T)

For the square, all 4 sides are equal (length S)

Also T = S + 4; P_t = P_s + 4; P_t = 4S + 4

P_t = 3T = 3(S + 4) = 4S + 4

3S + 12 = 4S + 4

S = 8 in.

T = 12 in.

Check; P_t = 3(12) = 36 in; P_s = 4(8) = 32 in.