The floor of a shed given on the right has an area of 55 square feet. The floor is in the shape of a rectangle whose length is 1foot less than twice the width. Find the length and the width of the floor of the shed.

The answer to your question is: l = 10 ft; w = 11/2 ft

Step-by-step explanation:

Data

Area = 55 ft²

length = l

width = w

l = 2w - 1

Process

Area = l x w

Area = (2w - 1) w

Area = 2w² - w

2w² - w - 55 = 0 Solve the quadratic equation

2w² + 10w - 11w - 55 = 0

2w (w + 5) - 11 (w + 5) = 0

(w + 5) (2w - 11) = 0

w1 = - 5 w2 = 11/2 There is not negative width, so the answer is 11/2 ft

l = 2 (11/2) - 1

l = 11 - 1

l = 10 ft

Area = (10) (11/2) = 110 / 2 = 55 ft²