Question

The area of a rectangle is 27 m”, and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.

Answer 1

`L = 6` --- Length

`W = 4.5` --- Width

Explanation:

Given

Let:
`L = Length; W = Width`

`Area = 27m^2`

`L = 2W- 3m`

Required

Find the dimensions of the rectangle

Area (A) is calculated as:

`A = L * W`

This gives:

`27 = (2W - 3) * W`

Open bracket

`27 = 2W^2 - 3W`

Express as a quadratic function

`2W^2 - 3W - 27 = 0`

Expand

`2W^2 + 6W - 9W - 27 = 0`

Factorize:

`2W(W + 3) - 9(W + 3) = 0`

`(2W - 9)(W + 3) = 0`

This gives:

`2W - 9 = 0\ or\ W + 3 = 0`

`2W = 9 \ or\ W = -3`

Width can not be negative.

So:

`2W = 9`

`W = 4.5`

Recall that:

`L = 2W- 3m`

`L = 2 * 4.5 - 3`

`L = 6`