Question

The rectangle below has an area of x^2-4x-12 square meters and a length of x+2what expression represents the width of the rectangle?

Answer 1

x^2 - 4x - 12
x - 6
x +2

If L equals to x + 2 than W will equal to x - 6

Answer 2

Answer:

The width is x-6.

Step-by-step explanation:

Givens:

• Area of the rectangle $x^2-4x-12$ square meters.
• The length is $x+2$

We know that, the are of a rectangle is:

$A=(length)(width)$

$x^2-4x-12=(x+2)w$

$\frac{x^2-4x-12}{x+2}=w$

Now, to solve this, we factorize the numerator.

$x^2-4x-12=(x-a)(x+b)$

So, we need to find two number which product is 12 and difference is 4.

$x^2-4x-12=(x-6)(x+2)$

Now, we replace this result in the fraction expression:

$\frac{x^2-4x-12}{x+2}=w\\w=\frac{(x-6)(x+2)}{(x+2)}\\w=x-6$

Therefore, the width is x-6.