The side of an equilateral triangle is 2 inches shorter than the side of a

square. The perimeter of the square is 30 inches more than the perimeter

of the triangle. Find the length of a side of the triangle.

Hi, Mercedes.

The key to figuring this one out is to draw your two shapes.

Since all three sides of an equilateral triangle have the same measure, label all three sides with an x.

Since all four sides of a square have the same measure, we will label them with the same expression as each other: x + 2. The reason the expression is x + 2 is because the triangle's sides are two inches shorter than the rectangle's sides (so the rectangle's
sides are two inches longer).

Now address Perimeter. To find the perimeter, add the sides together.

Triangle: x + x + x = 3x

Square: (x + 2) + (x + 2) + (x + 2) + (x + 2) = 4(x + 2) or 4x + 8

The Perimeter of the square is 30 inches more than the Perimeter of the triangle.

P (square) = P (triangle) + 30

4x + 8 = 3x + 30

This should help in setting up your equation.

*Note - you could have labeled the triangle's sides with (x - 2) and the square's sides with x.

In that case, your equation would be: 4x = 3(x - 2) + 30.

Either way will work.