How to find the dimensions

Question

The area of a rectangle is 35yd square and the length is 8yd less than 3 times the width. Find the dimension of the rectangle

Answer 1

A = Area

L= Length

W = Width

A = LW

L = 3W - 8

A = W(3W - 8) = 3W^2 - 8W = 35

3W^2 - 8W - 35 = 0 = (3W + 7)(W - 5)

3W + 7 = 0

3W = -7

W = -7/3 yards

Note: W will be positive, because all distances are positive so W does not equal -7/3

W - 5 = 0

W = 5 yards

L = 3(5) - 8 = 15 - 8 = 7 yards