Question

The area of a rectangle is x²+2x-24. If the width of the rectangle is x-4, what is its length?

Answer 1

x+6

Explanation:

The formula for area is:

`Area=l*w`

First, let's factor the area. We need to find two numbers that have a product of -24 and a sum of 2.

-4*6=-24

-4+6=2

We can substitute 2x with -4x and 6x:

`x^2-4x+6x-24`

Factor each half separately:

`x(x-4)+6(x-4)`

Since x and 6 both are being multiplied by x-4, we can combine them to get:

`(x-4)(x+6)`

Now, we can substitute this back into the original area equation to solve for the length:

`(x-4)(x+6)=(x-4)length`

Divide both sides by x-4

`l=x+6`