Question

The area of a rectangle is x2 - 2x - 15 and the length of the rectangle is x + 3. Find the width of the rectangle.

Answer 1

Width of the rectangle is (x-5)

Explanation:

We know that, the product of length and width gives the area of the rectangle.

The area of a rectangle is given as,

`\Rightarrow \text{Area of rectangle}=\text{Length}* \text{Width}`

`\Rightarrow \text{Width}=\frac{\text{Area of rectangle}}{\text{Length}}`

Factoring the area,

`=x^2-2x-15`

`=x^2-5x+3x-15`

`=x(x-5)+3(x-5)`

`=(x+3)(x-5)`

Putting it in the equation,

`\Rightarrow \text{Width}=((x+3)(x-5))/((x+3))=(x-5)`

Answer 2

Area of the rectangle= L* w

`x^(2) -2x-15`
On expanding;

`x^(2) -5x+3x-15`
=x(x-5)+3(x-5)
=(x+3)(x-5)
The width is (x-5)