Question

The length a rectangle is 4 feet less than three times the width, and the area of a rectangle is 55 ft.? find the dimensions of the rectangle

Answer 1

Answer:

width = 5 feet

length = 11 feet

Step-by-step explanation:

Using one variable and setting up two expressions equal to the total area of the rectangle will determine the dimensions of the rectangle.

w = width

l = '4 feet less than three times the width' or 3w - 4

Area = length x width

A = w(3w - 4) = 55

Distribute: 3w² - 4w  = 55

Set equation equal to '0': 3w² - 4w - 55 = 0

Multiply 3 x -55 = -165 and find two factors with a product of -165 and sum of -4:  -15 and 11.

3w² - 15w + 11w - 55

Group and find the GCF (greatest common factor):

3w(w - 5) + 11(w - 5)

(3w + 11)(w - 5) = 0

3w + 11 = 0    and w - 5 = 0

w = -11/3 not possible to have negative measurement

w = 5 feet

Solve for length:  3(5) - 4 = 11 feet