The width of a rectangle is 6 inches less than 3/4 the length. If the perimeter of the rectangle is 44 inches, find the dimensions of the rectangle.

Answer 1

Hello Malia. This is a classic substitution problem, and we start by defining the variables:

W = Width, L = Length, P = Perimeter

We know that the that the perimeter of the area [Equation 1] P = 2W+2L = 44

Based on the word problem we know that [Equation 2] W = (3/4)L - 6.

Substitute the expression for W from Equation 2 into Equation 1:

1. 2((3/4)L-6)+2L = 44
2. (6/4)L -12+2L = 44
3. 3.5L-12 = 44
4. 3.5L = 56
5. L = 16

Substitute the value for L into Question 2 to find W:

1. W = (3/4)(16)-6
2. W =6

The dimensions of the rectangle would be W = 6 in, L = 16 in.