An equilateral triangle is a triangle in which all three sides are equal.

Assuming the lengths of the sides of the equilateral triangle are 'a' the perimeter is p1=3a.

Let 'b' the length of the side of the square then the perimeter is p2 = 4b.

Now we can write the following equations:

p1 = p2 + 13 (perimeter of an equilateral triangle is 13 inches more than the perimeter of a square)

a = b + 7 (the side of the triangle is 7 inches longer than the side of the square)

We need to find a and b. Of course a and b must be non-negative.

Lets solve the system of equations

p1 = p2 + 13 substitute the values for p1 and p2

a = b + 7

we get

3a = 4b + 13

a = b + 7 substitute the value for a in the above equation

3 (b+7) = 4b + 13 lets solve this equation to find b

3b + 3*7 = 4b + 13

3b + 21 = 4b + 13

4b + 13 = 3b + 21

4b - 3b = 21 - 13

b = 8 in

a = b + 7 = 8 + 7 = 15 in

The side of the triangle is 15 inches long.