Chapter 11.1, Problem 4CCYP

To determine

Find base and height of the parallelogram.

Answer to Problem 4CCYP

The base is 12 feet and height is 6 feet.

Explanation of Solution

Given:

The base of a parallelogram is twice its height .The area of the parallelogram is 72 square feet.

Formula Used:

Area of a parallelogram with base b and height h is :

  $A=bh$

Calculation:

Let the height of the parallelogram be h feet.

Since the base is twice the height,so, the base, b of the parallelogram is 2h .

  $\begin{array}{l}A=bh\\ \Rightarrow 72=(2h)h\mathrm{...........}[A=72,b=2h]\\ \Rightarrow 72=2h^2\\ \Rightarrow h^2=\frac{72}{2}\mathrm{...........}[\text{divide each side by 2]}\\ \Rightarrow h^2=36\\ \Rightarrow h=\sqrt{36}\mathrm{..........}[\text{take square root each side]}\\ \Rightarrow h=6\text{ feet}\\ \Rightarrow b=2h=2(6)=12\text{ feet}\end{array}$

So, the base is 12 feet and height is 6 feet.