Question

The area of the parallelogram is 150 sq. in. What is the perimeter given the height is 6 and the base is 4x-3?

Answer 1

The formula for area of a parallelogram is `A = b xx h`.

`A = b xx h`

`150 = 6(4x- 3)`

`150 = 24x - 18`

`168 = 24x`

`x = 7`

So, the base measures `4(7) - 3 = 25` inches.

Let's draw a diagram.

So, we need to find `a` in order to find the perimeter. We can visualize a parallelogram as a square with two triangles on the side. The square, in this case, has a side length of `6` inches. So, the right triangle on the left has a base measuring `25 - 6 = 19`.

By pythagorean theorem:

`19^2 + 6^2 = a^2`

`397 = a^2`

`a = sqrt(397)`

The perimeter is simple to find now:

`P = 2(a + b)`

`P = 2(sqrt(397) + 25)`

`P ~= 89.85" inches"`

Hopefully this helps!