Answer: length = 25 feet
Width = 17 feet
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
The area of a room is 425 square feet. The length is (x + 11) feet and the width is (x + 3) feet. It means that
(x + 11)(x + 3) = 425
x² + 3x + 11x + 33 = 425
x² + 14x + 33 - 425 = 0
x² + 14x - 392 = 0
x² + 28x - 14x - 392 = 0
x(x + 28) - 14(x + 28) = 0
x - 14 = 0 or x + 28 = 0
x = 14 or x = - 28
The only possible value for x is 14. Hence,
Length = x + 11 = 14 + 11 = 25 feet
Width = x + 3 = 14 + 3 = 17 feet
