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

Hint: Let the length of the sides of the triangle is $a,b$ and $c$. The perimeter of any shape is the sum of all of its sides. Therefore, the perimeter of the triangle is $a + b + c$. According to the given conditions substitute all the values and evaluate the length of the side.

Complete step-by-step answer:
We are given that a triangle has a perimeter of $13$ and one side of length $3$ and the length of the two remaining sides are equal.
 We have to evaluate the length of each side.
Let the length of the sides of the triangle is $a,b$ and $c$.
According to our question,
$a = 3$ and $b = c$.
Let the perimeter of the triangle be $p$.
According to the question,
$p = 13$
We know that the perimeter of the triangle is the sum of all the sides.
Therefore, $p = a + b + c$
Substitute all the values and evaluate the length of the side.
$
   \Rightarrow 13 = 3 + b + b \\
   \Rightarrow 2b + 3 = 13 \\
   \Rightarrow 2b = 13 - 3 \\
   \Rightarrow 2b = 10 \\
   \Rightarrow b = 5 \\
 $
The length of two sides are equal. Therefore, $b = c = 5$
Therefore, the length of each equal side is $5$.
Hence, option (B) is correct.

Note:
We can solve this question by another method which is show below:
We can get our answer by checking the options.
Since, the length of the two sides are equal therefore, multiply the options by $2$ and add it to the length of the third side that is $3$.
If the sum will be $13$ then that option will be your answer.
$ \Rightarrow 2 \times 5 + 3 = 13$
Hence, option (B) is correct.