Question

The area of a rectangle is 28m^2, and the length of the rectangle is 5 meters less than three times the width. Find the dimensions of the rectangle. L:W:

Answer 1

The area of a rectangle is given by the formula

`A=L*W`

where

A=28 m2

L=3W-5

substitute given values in the formula

`\begin{gathered} 28=(3w-5)W \\ 28=3w^2-5w \\ 3w^2-5w-28=0 \end{gathered}`

Solve the quadratic equation

Using the formula

we have

a=3

b=-5

c=-28

substitute

`w=(-(-5)\pm√(-5^2-4(3)(-28)))/(2(3))`
`w=(5\pm19)/(6)`

The solutions for w are

w=4 and w=-2.33 ( is not a solution because is a negative number)

so

The width w=4 m

Find out the value of L

L=3w-5=3(4)-5=7 m

therefore

L=7 m

W=4 m