Question

The length of a rectangle is 3 m less than double the width, and the area of the rectangle is 27 m'. Find the dimensions of the rectangle.Length: Width:

Answer 1

From the question;

The length of a rectangle is 3 m less than double the width

`\begin{gathered} \text{let width = w } \\ \text{therefore} \\ \text{length = (2w - 3)m} \end{gathered}`

The are of the rectangle is 27 square meters

therefore

`\begin{gathered} \text{Area = length }*\text{ width} \\ \text{27 = (2w - 3)w} \\ 27=2w^2-3w^{} \\ 2w^2-3w^{}\text{ - 27 = 0} \\ by\text{ factorising} \\ 2w^2+6w-9w\text{ - 27 = 0} \\ 2w(w\text{ + 3) }-9(w\text{ + 3) = 0} \\ (2w-9)(w^{}\text{ + 3) = 0} \\ 2w-9=0^{}\text{ or w + 3 = 0} \\ w\text{ = }(9)/(2)\text{ or w}^{}\text{ = -3} \end{gathered}`

Since width of a rectangle can not be negative then

the width of the rectangle = 9/2m

The lentgh will be

`\begin{gathered} \text{Length of rectangle = (2w -3})m \\ \text{Length of rectangle = (2(}(9)/(2))\text{ - 3})m \\ \text{Length of rectangle = (9 - 3})m \\ \text{Length of rectangle = 6m} \end{gathered}`

Therefore the length of the rectangle is 6m