Q46. - Algebra 2

Question

A parallelogram with an area of $6x^2-7x-5$ square units has a base of $3x-5$ units. Determine the height of the parallelogram.

Step-by-Step Solution

Answer

The height of the parallelogram is $2x+1$ units.

Step 1. Given Information.

Given a parallelogram has an area of $6x^2-7x-5$ square units and a base of $3x-5$ units.

The height of the parallelogram is to be determined.

Step 2. Explanation .

The area of a parallelogram is given by $A=base\times height$.

Plugging the given values in the equation:

$\begin{array}{l}A=base\times height\\ 6x^2-7x-5=\left(3x-5\right)\times h\\ h=\frac{6x^2-7x-5}{3x-5}\\ h=\frac{6x^2+3x-10x-5}{3x-5}\\ h=\frac{3x\left(2x+1\right)-5\left(2x+1\right)}{3x-5}\\ h=\frac{\left(3x-5\right)\left(2x+1\right)}{3x-5}\\ h=2x+1\end{array}$

Step 3. Conclusion .

Hence, the height of the parallelogram is $2x+1$ units.