Question

The length of a rectangle is 7 inches less than twice the width of the rectangle. If the area of the rectangle is 60 square inches, what is the width of the rectangle?

Answer 1

`Length=8inches\\Width=7.5 inches`

Explanation:

Let the width of the rectangle be 'w' inches

Length of the rectangle= (2w-7) inches

Area of the rectangle=
`60 inches^2`

Area of the rectangle= Length*Width

`60=(2w-7)(w)\\\\60=2w^2-7w\\\\2w^2-7w-60=0`

Making the factors of the equation:

`2w^2+8w-15w-60=0\\\\`

Taking common from the equation;

`2w(w+4)-15(w+4)=0\\\\(w+4)(2w-15)=0`

`w+4=0\\\\w=-4`

OR

`2w-15=0\\2w=15\\w=15/2\\w=7.5inches`

As the width of the rectangle cannot be negative, so,

`Width(w)= 7.5 inches`

`Length=2w-7=2(7.5)-7=15-7=8 inches`

`Length=8inches\\Width=7.5 inches`