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)`

Step-by-step 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 * 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!