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?

Question

asked Feb 26, 2022 209k views

1 Answer

Chris Ruppel · Answer 1 · 2022-03-02T18:06:22+0000

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
.