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

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

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Answer 1 · 2016-10-26T13:30:11

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

$A = b \times h$ $A = b xx h$

$150 = 6 (4 x - 3)$ $150 = 6(4x- 3)$

$150 = 24 x - 18$ $150 = 24x - 18$

$168 = 24 x$ $168 = 24x$

$x = 7$ $x = 7$

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

Let's draw a diagram.

enter image source here

So, we need to find $a$ $a$ 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 $6$ $6$ inches. So, the right triangle on the left has a base measuring $25 - 6 = 19$ $25 - 6 = 19$ .

By pythagorean theorem:

$19^{2} + 6^{2} = a^{2}$ $19^2 + 6^2 = a^2$

$397 = a^{2}$ $397 = a^2$

$a = \sqrt{397}$ $a = sqrt(397)$

The perimeter is simple to find now:

$P = 2 (a + b)$ $P = 2(a + b)$

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

$P ≅ 89.85 inches$ $P ~= 89.85" inches"$

Hopefully this helps!

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

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