Question

The sides of a triangle are 56 cm, 60 cm and 52 cm. Area of the triangle is
(a) 1322 cm²
(b) 1311 cm²
(c) 1344 cm²
(d) 1392 cm²

Answer 1

Given:
The sides of a triangle are 56 cm, 60 cm and 52 cm.

Using Heron's formula:
If a, b and c are three sides of a triangle, then
area of the triangle = $\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$ , where $s=\frac{a+b+c}{2}$.


Here, $s=\frac{56+60+52}{2}=\frac{168}{2}=84$

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{84\left(84-56\right)\left(84-60\right)\left(84-52\right)} \\ =\sqrt{84\left(28\right)\left(24\right)\left(32\right)} \\ =\sqrt{3\times 7\times 2\times 2\left(7\times 2\times 2\right)\left(3\times 2\times 2\times 2\right)\left(2\times 2\times 2\times 2\times 2\right)} \\ =\left(3\times 7\times 2\times 2\times 2\times 2\times 2\times 2\right) \\ =1344{\mathrm{cm}}^2 \end{gathered}$$

Hence, the correct option is (c).