A rectangular carport has area of 150 squarefeet. The width of the carport is five feet less than twice its length. Find the length and the width of the carport.

The length and with of the carport are  10 ft and 15 ft respectively.

Area of the rectangular carport = 150 ft²

let

l = length

width = w = 2l - 5

The length and width can be found below

area = 150 ft²

area  = lw

150 = l(2l - 5)

150 = 2l² - 5l

2l² - 5l - 150 = 0

using quadratic formula,

2l² - 5l - 150 = 0

- b±√b² - 4ac / 2a

where

a = 2

b = -5

c = -150

5±√25 + 1200 / 4

5 ±  √1225 / 4

5 ± 35 / 4

Therefore,

l  = 10 or - 15 / 2

The length can only be positive

so, l = 10 ft

150 = lw

w = 150 / 10

width = 15 ft

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The length of the carpet is 10 feet and the width of the carpet is 15 feet

Explanation:

Given:

Area of the carpet, A = 150 ft²

Let x be the length of the carpet

Let y be the width of the carpet

According to the question:

width, y = 2x - 5                      -1

We know:

Area of rectangle = length X width

On substituting the value we get:

150 = (x) (2x - 5)

150 = 2x² - 5x

2x² - 5x - 150 = 0

Solving the quadratic equation we get

x = 10 feet

Substituting x = 10 ft in equation 1 we get:

y = 2x - 5

y = 2(10) - 5

y = 15 feet

Therefore, the length of the carpet is 10 feet and the width of the carpet is 15 feet