Question

The rectangle below has a area x^2-x-72 square meters and a length of x+8 meters what expression represents the width of the rectangle

Answer 1

ANSWER

$w = (x - 8)$

EXPLANATION

The given rectangle has area,

$A = {x}^{2} - x - 72 \: {m}^{2}$

It was given to us that, the length of the rectangle is l=(x+8)

To find the width, we need to factor, the expression for the area.

We split the middle term to get,

$A = {x}^{2} - 9x + 8x- 72$

We now factor by grouping;

$A = x(x - 9) + 8(x- 9)$

$A = (x + 8)(x - 9)$

We know that area of a rectangle is

$A = l \times w$

Hence the width of the rectangle is,

$w = (x - 8)$

Answer 2

Hello!

The answer is:

The expression that represents the width of the rectangle is:

$width=x-9$

Why?

We know that the area of a rectangle is equal to:

$A=length*width$

We are given the function that represents the area of the rectangle and one of its sides, the length is equal to (x+8)

So, rewriting we have:

$x^{2}-x-72 =(x+8)*width$

The coefficients of the variables of the given function are:

$x^{2}=1\\-x=-1$

Now, to find the width, we need to find two numbers which its product gives as result "-72" and its addition gives as result the coefficient of the linear term of the function (x), its "-1".

Then,

We know that,

$(-9)*(8)=-72\\-9+8=-1$

So, the factors of the given function are:

$x^{2}-x-72 =(x+8)*(x-9)$

Since, we already know that the length corresponds to "x+8", we know that the width corresponds to "x-9".

Proving that the factors are right,

Applying the distributive property, we have:

$(x+8)(x-9)=x^{2}-9x+8x-72=x^{2}-x-72$

Hence, the equation is satisfied and we can conclude that:

$length=x+8\\width=x-9$

Have a nice day!