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

Oct 26, 2016

The formula for area of a parallelogram is $A = b \times h$.

$A = b \times h$

$150 = 6 \left(4 x - 3\right)$

$150 = 24 x - 18$

$168 = 24 x$

$x = 7$

So, the base measures $4 \left(7\right) - 3 = 25$ 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:

$P = 2 \left(a + b\right)$

$P = 2 \left(\sqrt{397} + 25\right)$

$P \cong 89.85 \text{ inches}$

Hopefully this helps!