Question

The area of a rectangle is (x^3 - 5x^2 + 3x - 15), and the width of the rectangle is (X2 + 3). If area = length x width, what

is the length of the rectangle?

Answer 1

Given:

Area of a rectangle =
`x^3-5x^2+3x-15`

Width of rectangle =
`x^2+3`

To find:

The length of the rectangle.

Solution:

The area of a rectangle is:

`A=l* w`

Where, l is length and w is the width.

It is can be written as:

`(A)/(w)=l`

`l=(A)/(w)`

Putting
`A=x^3-5x^2+3x-15` and
`w=x^2+3`, we get

`l=(x^3-5x^2+3x-15)/(x^2+3)`

`l=(x^2(x-5)+3(x-5))/(x^2+3)`

`l=((x^2+3)(x-5))/(x^2+3)`

`l=x-5`

Therefore, the length of the rectangle is
`x-5`.