Question

The lengths of the three sides of a triangle are $20cm$, $16cm$ and $12cm$. The area of the triangle is

• A. $96c{m}^2$
• B. $144c{m}^2$
• C. $120c{m}^2$
• D. $160c{m}^2$

Answer 1

The correct option is A

$96c{m}^2$

Explanation for the correct option:

Find the area of a triangle

To find the area of the triangle, we will use Heron's formula.

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Where $s=\frac{a+b+c}{2}$ and $a,b,c$ are the sides of the triangle.

So, the semi-perimeter of the triangle,

$$\begin{gathered} s=\frac{20+16+12}{2} \\ \Rightarrow s=\frac{48}{2} \\ \Rightarrow s=24cm \end{gathered}$$

Thus, the area of the triangle will be,

$$\begin{gathered} A=\sqrt{s(s-a)(s-b)(s-c)} \\ \Rightarrow A=\sqrt{24(24-20)(24-16)(24-12)} \\ \Rightarrow A=\sqrt{24\left(4\right)\left(8\right)\left(12\right)} \\ \Rightarrow A=96c{m}^2 \end{gathered}$$

Hence, the correct option is $\left(a\right)96c{m}^2$.