Question

In the diagram below, the perimeter of the triangle is equal to the perimeter of the square. What is the length of a side of the square?

Answer 1

The perimeter of each is the sum of the lengths of its sides.

Triangle Perimeter = 16 + 4x-3 +3x = 7x+13

Square Perimeter = 2x +2x +2x +2x = 8x

If these are equal, you have

$7x+13=8x\\\\13=x\qquad \mbox{subtract 7x}\\\\26=2x\qquad \mbox{multiply by 2}$

The length of a side of the square is 26 units.