Question

The difference between the semi-perimeter and the sides of triangle ABC are 8 cm, 7 cm and 5 cm,

respectively. Find its semi-perimeter.A 30B 22C 35D 20

Answer 1

Let a, b and c be the lengths of sides of a triangle and S be its perimeter.
According to the given parenthesis, the difference between the sides and its semi perimeter is given by;
$$\begin{gathered} S-a=8\Rightarrow a=S-8 \\ S-b=7\Rightarrow b=S-7 \\ S-c=5\Rightarrow c=S-5 \end{gathered}$$
Now, the perimeter of triangle is given by;
$$\begin{gathered} S=\frac{a+b+c}{2} \\ \Rightarrow S=\frac{\left(S-8\right)+\left(S-7\right)+\left(S-5\right)}{2} \\ \Rightarrow 2S=3S-20 \\ \Rightarrow 3S-2S=20 \\ S=20 \end{gathered}$$
Therefore the perimeter of triangle is 20 cm.