The perimeter of an equilateral triangle is 7 inches more than the perimeter of a square,and the side of the triangle is 5 inches longer than the side of square.Find the side of the triangle.

Let triangle side length be T and square side length be S.

3T = 4S + 7
T = S + 5

4T = 4S + 20

Subtract the first equation from the last to get T

To find the side of the equilateral triangle, we need to set up equations based on the given information and solve them step-by-step. Let's begin:

Let's assume the side length of the square is "x" inches.
Since the side of the triangle is 5 inches longer than the side of the square, the side length of the triangle would be "x + 5" inches.

The perimeter of a square is calculated by multiplying the side length by 4. Therefore, the perimeter of the square would be 4x inches.

The perimeter of an equilateral triangle is calculated by multiplying the side length by 3. So, the perimeter of the triangle would be 3(x + 5) inches.

The problem states that the perimeter of the equilateral triangle is 7 inches more than the perimeter of the square. So, we can set up the equation:

3(x + 5) = 4x + 7

Now, let's solve the equation step-by-step:

1. Distribute the 3 to (x + 5):

3x + 15 = 4x + 7

2. Move all the variables (terms with "x") to one side of the equation and the constants to the other side:

3x - 4x = 7 - 15

Simplify:

-x = -8

3. Divide both sides of the equation by -1 to solve for "x":

x = 8

Therefore, the side length of the square is 8 inches.

To find the side length of the equilateral triangle:

x + 5 = 8 + 5 = 13

Therefore, the side length of the equilateral triangle is 13 inches.