Question

In $△ABC,AB=AC=4.5\text{cm, and}\angle BAC={72}^{\circ }$ lies inside a regular pentagon such that the side $BC$ is one of the sides of the pentagon. What will be the perimeter of the pentagon?

• A. $26.5\text{cm}$
• B. $22.5\text{cm}$
• C. $29.5\text{cm}$
• D. $25.7\text{cm}$

Answer 1

The correct option is A $26.5\text{cm}$

To find the length of the unknown side $BC$, we construct the triangle using the SAS criterion as shown below:

1. First, let’s draw a line segment $AB=4.5\text{cm}$.


2. Next, we’ll draw an angle ${72}^{\circ }$ at vertex $A$.


3. Cut an arc of radius $4.5\text{cm}$ with $A$ as the center to get point $C$.

4.Connect $BC$.

Measuring $BC$ using a ruler, we get: $BC\simeq 5.3\text{cm}$.

Since $BC$ is one of the sides of the regular pentagon, all the other sides of the pentagon are also of length $5.3\text{cm}$

Perimeter of the pentagon = $5.3\times 5=26.5\text{cm}$