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

Answer:

x+6

Step-by-step 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

$l=x+6$