Question

The length of a rectangle is 7 more than twice the width, and the area of the rectangle is 99 yd^2 . Find the dimensions of the rectangle

Answer 1

Width of a rectangle =
`(11)/(2)` yards

Length of a rectangle =
`18` yards

Explanation:

Let width be
`x` yards.

Length of a rectangle =
`7+2x`

Area of a rectangle = length × width

Put area of the rectangle as
`99\,\,yd^2`

Therefore,

`99=x(7+2x)\\\\99=7x+2x^2\\\\2x^2+7x-99=0\\\\2x^2+18x-11x-99=0\\2x(x+9)-11(x+9)=0\\\\(2x-11)(x+9)=0\\\\x=(11)/(2),x=-9`

Being a dimension,
`x` cannot be negative.

So,

`x=(11)/(2)`

Width =
`x=(11)/(2)` yards

Length of a rectangle =
`7+2x=7+2((11)/(2))=7+11=18` yards