Q12. - Algebra 1

Question

Find the perimeter of following figure.

Step-by-Step Solution

Answer

The perimeter of figure is $18\frac{1}{2}\text{\hspace{0.17em}\hspace{0.17em}inches}$.

Step 1. Given information.

Lengths of two sides of the figure are $6\frac{1}{2}$ inch and $2\frac{3}{4}$ inch.

Step 2. Write the concept.

The given figure is a rectangle.

So,

The perimeter of a rectangle is given by:

$P=2\left(\text{Length}+\text{Width}\right)$

Step 3. Write the expression for Perimeter.

Length of rectangle $=6\frac{1}{2}$ inch

Width of rectangle $=2\frac{3}{4}$ inch

The perimeter of figure is given by:

$P=2\left(6\frac{1}{2}+2\frac{3}{4}\right)$

Step 4. Simplify the expression.

The expression $P=2\left(6\frac{1}{2}+2\frac{3}{4}\right)$ can be simplified as in below.

$\begin{array}{c}P=2\left(6\frac{1}{2}+2\frac{3}{4}\right)\\ =2\left(\frac{13}{2}+\frac{11}{4}\right)\end{array}$

Since,

$\begin{array}{c}\frac{13}{2}+\frac{11}{4}=\frac{13\times 2}{2\times 2}+\frac{11}{4}\\ =\frac{26}{4}+\frac{11}{4}\\ =\frac{26+11}{4}\\ =\frac{37}{4}\end{array}$

So,

$\begin{array}{c} P=2\left(\frac{37}{4}\right)\\ =2\times \frac{37}{4}\\ =\frac{37}{2}\\ =18\frac{1}{2}\end{array}$

Therefore, the perimeter of triangle is $18\frac{1}{2}$ inches.