Question

Find the value of $c$ in a triangle if the semi perimeter is $13$ and the values of $a$ and $b$ are $8$ and $7$ respectively.

Answer 1

Find the value of $c$ in a triangle using the formula for perimeter

Let $P$ be the perimeter of the triangle

Let, $S$ be the semi perimeter of the triangle.
The semi perimeter of the triangle is given to be$S=13cm$
The three sides of the triangle are $a$, $b$ and $c$
The values of $a=8cm$ and $b=7cm$ are given values
To find the value of $c$ use the perimeter
The perimeter of the triangle is twice the semi perimeter
$P=2S$

Substituting the value of $S$
$$\begin{gathered} P=2\left(13\right) \\ P=26cm \end{gathered}$$
As the perimeter of the triangle is the sum of the three sides.
$P=a+b+c$
Substituting the values in the above equation

$$\begin{gathered} \Rightarrow 26=8+7+c \\ \Rightarrow 26=15+c \end{gathered}$$
$\Rightarrow$ $c=11$

Hence the value of $c$ is $11$