Question

Each of the equal sides of an isosceles triangle is $13cm$ and its base is $24cm$. The area of the triangle is

• A. $156c{m}^2$
• B. $60c{m}^2$
• C. $78c{m}^2$
• D. $120c{m}^2$

Answer 1

The correct option is B

$60c{m}^2$

Explanation for the correct option:

Find the semi-perimeter of the triangle

Let the sides of the isosceles triangle be $a=13cm,b=13cm,c=24cm$.

It is known that the semi-perimeter of the triangle can be given as: $s=\frac{a+b+c}{2}$

Where $a,b,c$are the sides of the triangle.

Now, the semi-perimeter will be,

$$\begin{gathered} s=\frac{13+13+24}{2} \\ \Rightarrow s=25cm \end{gathered}$$

Find the area of the triangle

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

Heron's formula can be given that: $A=\sqrt{s(s-a)(s-b)(s-c)}$

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

Now, the area of the triangle will be,

$$\begin{gathered} A=\sqrt{25(25-13)(25-13)(25-24)} \\ \Rightarrow A=\sqrt{25\left(12\right)\left(12\right)\left(1\right)} \\ \Rightarrow A=60c{m}^2 \end{gathered}$$

Hence, the correct option is (b) $60c{m}^2$.