A builder cuts a rectangular hole in a ceiling to install an exhaust fan. The width is 3 inches less than the length and the area is 180inches squared. Find the length and width of the hole

length of hole = 15 inches

Width of hole = 12 inches

Step-by-step explanation:

Let L represent the length of the hole.

Let W represent the width of the hole.

The width is 3 inches less than the length. It means that

W = L - 3

The formula for determining the area of a rectangle is expressed as

Area = LW

The area of the rectangular hole is 180inches squared. It means that

LW = 180- - - - - - - - - - 1

Substituting W = L - 3 into equation 1, it becomes

L(L - 3) = 180

L² - 3L = 180

L² - 3L - 180 = 0

L² + 12L - 15L - 180 = 0

L(L + 12) - 15(L + 12) = 0

L - 15 = 0 or L + 12 = 0

L = 15 or L = - 12

Since the length cannot be negative, then L = 15

W = L - 3 = 15 - 3

W = 12