Question

A triangle has a perimeter of $13$ and one side of length $3$. If the lengths of the other two sides are equal, what is the length of each of them?

• A. $4$
• B. $5$
• C. $6$
• D. $7$
• E. $8$

Answer 1

Answer: (B)

$5$

Let ${}^{\prime }{x}^{\prime }$ be the length of one of the equal sides.

The perimeter of the triangle with sides a$,b$ and $c$ is $P=a+b+c$.

Substitute the values pf $P=13$ and $a=3,b=x,c=x$ in $P=a+b+c$ as shown below:

$\Rightarrow 13=3+x+x$

$\Rightarrow 13=3+2x$

$\to 2x=13-3$

$\Rightarrow 2x=10$

$\Rightarrow x=5$

Therefore, the length of each of the side is $5$.

Hence, option B is correct.