Answer: 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
