The perimeter is adding up all sides of a shape. Here we are told that the perimeter of the triangle is 41 inches. So we can make the equation:

Combine like terms(x + 3x = 4x):

We are also told that the perimeter of the rectangle is 66 inches. The formula for the perimeter of a rectangle is:

Plug in what we know:

Distribute 2 into the parenthesis:

So our system of equations is:


Let's use the substitution method to solve this system. Let's solve for 'x' in the second equation:

Subtract 14y to both sides:

Divide 6 to both sides:

Now let's plug this in for 'x' in the first equation:


Distribute:

Combine like terms:

Subtract 44 to both sides:

Divide -7/3 to both sides or multiply by its reciprocal -3/7:

So the solution to the system of equations is:

Plug these values in to find the length and width of the rectangle.
Length:



Width:

