Question

In a parallelogram ABCD, the length of the longer arm is equal to twice the length of the shorter arm....

Answer 1

Answer:

C. 12m

Explanation:

Let the length of the shorter arm = x

Since the length of the longer arm is equal to twice the length of the shorter arm;

• The length of the longer arm = 2x

• The area of triangle ABD = 18√3 m².

Given a triangle with two sides and the included angle, the area of the triangle is calculated using the formula below:

$\begin{gathered} \text{Area}=\frac{1}{2}ab\sin \theta \\ \implies\text{Area of triangle ABD =}\frac{1}{2}bd\sin A \end{gathered}$

Therefore:

$18\sqrt[]{3}=\frac{1}{2}(x)(2x)\sin (60\degree)$

We solve for x.

$\begin{gathered} 18\sqrt[]{3}=\frac{2x^2}{2}\times\sin 60\degree \\ 18\sqrt[]{3}=x^2\times\frac{\sqrt[]{3}}{2} \\ \text{Multiply both sides by }\frac{2}{\sqrt[]{3}} \\ 18\sqrt[]{3}\times\frac{2}{\sqrt[]{3}}=x^2\times\frac{\sqrt[]{3}}{2}\times\frac{2}{\sqrt[]{3}} \\ x^2=36 \\ x^2=6^2 \\ x=6 \end{gathered}$

Multiply x by 2 to get the length of the longer arm:

$2x=2\times6=12m$

The length of the longer arm is 12m.

C is the correct option.