Question

A rectangular carport has area of one 50 ft.The width of the carport is 5 feet less than twice its length. Find the length and width of the carport

Width= ? feet,
Length= ? feet

Answer 1

`Length = 10ft`

`Width = 15ft`

Explanation:

Given

`W= Width\\ L = Length`

`Area = 150`

`W=2*L- 5`

Required

Determine the dimension

Area is calculated as:

`Area = L * W`

So, we have:

`L * W = 150`

Substitute:
`W=2*L- 5`

`L * (2*L-5) = 150`

`L * (2L-5) = 150`

Open bracket

`2L^2 - 5L = 150`

Rewrite as:

`2L^2 - 5L - 150=0`

Expand

`2L^2 -20L + 15L - 150 = 0`

Factorize:

`2L(L -10) + 15(L - 10) = 0`

`(2L + 15) (L - 10) = 0`

Split

`2L + 15=0` or
`L -10 = 0`

Solve for L

`2L =-15` or
`L = 10`

L cannot be negative

So:

`L = 10`

Substitute
`L = 10` in
`W=2*L- 5`

`W = 2 * 10 - 5`

`W = 20 - 5`

`W = 15`

Hence:

`Length = 10ft`

`Width = 15ft`