Question

Sides of a triangle are in the ratio of $12:17:25$ and its perimeter is $540cm$. Find its area.

Answer 1

$\Rightarrow$Let $x$ be common ratio

$\therefore$ Sides of triangle will be: $12x,17x$ and $25x$

$\Rightarrow$Perimeter $=540cm$(given)

$\Rightarrow 12x+17x+25x=540cm$,

$\Rightarrow 54x=540cm$

$\Rightarrow x=10cm$$\therefore$ Sides of triangle: $a=120,b=170,c=250cms$

$\Rightarrow 2S=540$

$\Rightarrow S=270cm$

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

$=\sqrt{270(270-120)(270-170)(270-250)}{cm}^2$

$=\sqrt{270\times 150\times 100\times 20}{cm}^2$

$=\sqrt{3\times 3\times 3\times 10\times 5\times 3\times 10\times 100\times 5\times 4}{cm}^2$

$=3\times 3\times 10\times 10\times 5\times 2$

$A=9000{cm}^2$