Question

ABCD is a parallelogram. Find the value of each ratio.

$AD:perimeterofABCD$

Short answer

The simplest form of$AD:perimeterofABCD=3:16$

Step-by-step solution

Step 1. Given information.

According to the given figure is,

In parallelogram,

$\begin{array}{l}AD=BC=9\\ perimeterofABCD=AB+BC+CD+DA\\ =15+9+15+9\\ =48\end{array}$

Thus,

$\begin{array}{l}AD:perimeterofABCD=9:48\\ \frac{AD}{perimeterofABCD}=\frac{9}{48}\end{array}$

Step 2. Concept Used.

To write the fraction in simplest form, divide the numerator and denominator with the GCF (Greatest Common Factor).

Step 3. Now find the GCF.

Write the prime factors of numerator and denominator.

$\begin{array}{l}9=3\times 3\\ 48=2\times 2\times 2\times 2\times 3\end{array}$

Here GCF is3.

Step 4. Let’s divide the numerator and denominator with the GCF.

Here we will divide the numerator and denominator by.3

$\frac{9}{48}=\frac{9/3}{48/3}=\frac{3}{16}$

Therefore, the simplest form of the given ratio is$AD:perimeterofABCD=3:16$.