Question

If the area of a rectangle is 39 square feet and it has sides of `x-2` and `x+8`, what is the value of `x`?

Answer 1

`(x-2)(x+8)=39`

`x^2 +6x - 16 - 39 = 0`

`x^2 +6 x - 55 = 0`

`(x+11)(x-5) = 0`

`x=5 quad` We can skip `x=-11` which gives negative sides.

Check: `(5-2)(5+8)=(3)(13)=39 quad sqrt`

Answer 2

The value of `x` is 5.

Explanation:

The area of a rectangle can be determined by the following formula.

`A=l*w`

`l` stands for length or the longer side.
`w` stands for width or the shorter side.

Now, we can plug the values we are given into the equation.

`A=(x-2)*(x+8)`

The easiest way to multiply is to follow the acronym FOIL , which stands for First Outside Inside Last, and dictates the order in which you multiply these terms.

`A=x^2+8x-2x-16=x^2+6x-16`

Now, we can plug in the given value for the area.

`39=x^2+6x-16`

Next, we simplify by moving all terms to one side and factor the equation.

`0=x^2+6x-55`

Finally, we factor the equation. This means we reverse-FOIL, trying to determine the two things that we multiplied together.

`0=(x-5)*(x+11)`

If the equation ultimately equals zero, either `(x-5)` or `(x+11)` or both equal zero. Therefore, we set each equal to zero to find the value of `x`.

`x-5=0`
`x=5`

`x+11=0`
`x=-11`

Since `x` is a length, we know it cannot be negative. Thus, we can conclude that it equals 5.