Question

The length of the rectangle is 3ft less than twice the width,and the area of the rectangle is 27ft^2,find the diameter

Answer 1

The dimensions of rectangle are:

• width = w = 4.5 ft

• length = l = 6 ft

Explanation:

Let 'l' be the length and 'w' be the width of the rectangle

• The length 'l' of the rectangle is 3ft less than twice the width 'w'.

so

`l=2w-3`

Also, the area of the rectangle is 27ft^2.

`A=27\:ft^2`

As the area of the rectangle has the formula:

`\:A\:=\:l* w`

so

`27=\:l* w`

so the equation becomes

`27=\left(2w-3\right)* \:w`

`27=2w^2-3w`

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

`\left(w+3\right)\left(2w-9\right)=0`

if
`ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)`

`w+3=0\quad \mathrm{or}\quad \:2w-9=0`

`w=-3,\:w=(9)/(2)`

as the width can not be negative, so

`w=(9)/(2)=4.5` ft

As

`l=2w-3`

`l=2\left(4.5\right)-3`

`l=9-3`

`l=6`

So the dimensions of rectangle are:

• width = w = 4.5 ft

• length = l = 6 ft