Question

The length of a rectangle is 6 in. more than its width. Its area is 40 sq. in. How do you find the width of the rectangle?

Answer 1

The width of the rectangle is `4` inches.

Explanation:

We consider the width of the rectangle as `x` which will make the length `(x+6)`. Since we know the area, and the formula of a rectangle's area to be length `xx` breadth, we can write:

`x xx (x+6)=40`

Open the brackets and simplify.

`x^2+6x=40`

Subtract `40` from both sides.

`x^2+6x-40=0`

Factorise.

`x^2+10x-4x-40=0`

`x(x+10)-4(x+10)=0`

`(x-4)(x+10)=0`

`x-4=0` and `x+10=0`

`x=4` and `x=-10`

The only possibility in the above problem is that `x=4`.

That will make the width `4` and the length `(x+6)` which is `10`, and the area `(4xx10)` which is `40`.