Question

Question #8453f

Answer 1

The height would be 5 (units).

Explanation:

Since the area of a parallelogram is found by calculating base times height, we can do `5x+20` divided by `x+4` to find the height.

If this were a longer, more complicated problem with a possible remainder I would have done polynomial long division or synthetic division, but since the division isn't long or complex, we can simply divide it by putting the area over the base.

`(5x+20)/(x+4) rarr` `"area"/"base"`

Now we can simplify the fraction by seeing if there are common factors that can be divided out.

A GCF (5) can be factored out of `5x+20`. Thus, dividing each term by 5 would equal `x+4` because the `x+4` is a common factor in the numerator and denominator. (It would be like `(2*3)/2`, you can cancel the 2 for both sides.)

We are left with 5 as the height.

Answer 2

`color(green)(h = 5)`

Explanation:

Let Area = A, base = a, h = height

Given : `A = 5x + 20, a = x + 4`

`Area = a* h`

`h = A / a = (5x + 20) / (x + 4) =((5 * x) + (5 * 4)) / (x + 4)`

`=> (5 * cancel(x + 4)) / cancel(x + 4) = color(green)(5`