Question

The sides of a triangle are in the ratio of 13:14:15 and its perimeter is 84 cm. Then the area of the triangle is

• A. $136$ $c{m}^2$
• B. $236$ $c{m}^2$
• C. $336$ $c{m}^2$
• D. $436$ $c{m}^2$

Answer 1

Answer: (C)

$336$ $c{m}^2$

Let the sides of the triangle be $13a,14a,15a$.
Perimeter of the triangle $=$ Sum of all sides $=13a+14a+15a=42a$
Given, perimeter of the triangle $=84cm$

$\therefore 42a=84cm$

$a=2cm$
So, the sides of the triangle are $13a=26cm,14a=28cm,15a=30cm$.

Area of triangle with sides a, b, and c and $s=\frac{a+b+c}{2}$ is $\sqrt{s(s-a)(s-b)(s-c)}$.

For triangle with sides 26 cm, 28 cm and 30 cm, $s=\frac{26+28+30}{2}=42cm$
Area of the triangle with 26 cm, 28 cm and 30 cm $=\sqrt{42(42-26)(42-28)(42-30)}$

$=\sqrt{42\times 16\times 14\times 12}$

$=\sqrt{6\times 7\times 4\times 4\times 7\times 2\times 6\times 2}$

$=6\times 7\times 4\times 2=336{cm}^2$