Question

The lengths of the sides of a triangle are in the ratio $3:4:5$. Find the area of the triangle if its perimeter is $144$ cm.

Answer 1

Given:

Length of a ${\Delta }^{le}$ are in ratio $3:4:5$

perimeter $\left(p\right)=144cm$

Also given, to find the area of ${\Delta }^{le}$

$\iff 3x+4x+5x=144$

$12x=144\iff x=12$

so we get

$3x=3\left(12\right)=36;4\left(19\right)=48;54=5\left(12\right)=60$

$\therefore$ $s=\frac{1}{2}(a+b+c)$

$=\frac{1}{2}(36+48+60)$

$=\frac{1}{2}\times 144\iff 72cm$

Area of ${\Delta }^{le}$ with sides $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{72(72-36)(72-48)(72-60)}$

$=\sqrt{72\left(36\right)\left(24\right)\left(12\right)}$

$=\sqrt{2^2\times 3^2\times 2\times 2^2\times 3^2\times 2^2\times 2\times 3\times 2^2\times 3}$

$=2\times 3\times 2\times 3\times 2\times 2\times 3\times 2$

Area of ${\Delta }^{le}=864sq.cm$