Question

The side of a triangle with 3 equal sides is 7 inches shorter than the side of a square. the perimeter of the square is 39 inches more than the perimeter of the triangle. find the length of a side of the square.

Answer 1

The first thing we must do for this case is to define variables.
We have then:
x: sides of the triangle
y: sides of the square
The perimeter of the triangle is:

`p1 = 3x`
The perimeter of the square is:

`p2 = 4y`
We now write the system of equations that models the problem.
The side of a triangle with 3 equal sides is 7 inches shorter than the side of a square:

`x = y - 7`
The perimeter of the square is 39 inches more than the perimeter of the triangle:

`4y = 3x + 39`
Resolving the system graphically we have that the solution is the ordered pair:

`(x, y) = (11, 18)`
Note: See attached image for graphic solution.
Answer:
The length of a side of the square is:

`y = 18 inches`