We are given that the perimeter of an equilateral triangle is the same as the perimeter of a square.
Perimeter of a square = 4s
Perimeter of an equilateral triangle = 3s
We want to set both expressions equal to each other.
4s = 3s
The side length of a square is 2x + 1 and the side length of an equilateral triangle is 3x - 5. Substitute the value for each shape for s.
4(2x + 1) = 3(3x - 5) ⇒ 8x + 4 = 9x - 15 ⇒ x = 19
The side length of a square is 2(19) + 1 = 38 + 1 = 39.
The side length of an equilateral triangle is 3(19) - 5 = 57 - 5 = 52.
The perimeter of a square is 4(39) = 156.
The perimeter of an equilateral triangle is 3(52) = 156.
