Question

What is the value of x when the area of a parallelogram is 48 and the base height is x+6 and the height is x?

Answer 1

`x = -3+-sqrt(57)`

Explanation:

So let's list out the stuff we know:

Area of parallelogram: `48`.

Base: `x+6`

Height: `x`.

We know that the area of a parallelogram is base `*` height.

So we know that `x(x+6) = 48`.

We have one variable (`x`) and one equation, so we can solve this.

First, we want to distribute the `x` to everything inside the parenthesis:
`x^2 + 6x = 48`

Now we want to set one side of the equation equal to zero so we can solve by factoring. We can do this by subtracting `48` from both sides of the equation:
`x^2 + 6x - 48 = 0`

Now we need to factor to solve.

To factor this, we need 2 numbers that:
1. Multiply up to `-48`
2. Add up to `6`.

However, there are no 2 numbers that can do that, so we must use the quadratic formula, `(-b +- sqrt(b^2 -4ac))/(2a)`.
`x = (-6 +- sqrt(6^2-4(1)(-48)))/(2(1))`
`x = (-6 +- sqrt(36+192))/2`
`x = (-6 +- sqrt(228))/2`
`x = (-6 +- 2sqrt(57))/2`
`x = -3+-sqrt(57)`

Hope this helps!