Question

The sides of a triangle are $25m$, $39m$ and $56m$ respectively. Find the length of perpendicular from the opposite angle on the greatest sides.

• A. $56m$
• B. $60m$
• C. $15m$
• D. $12m$

Answer 1

The correct option is C $15m$

Let $a=25m,b=39m,c=56m$

We have, semi-perimeter, $s=\frac{a+b+c}{2}$

$s=\frac{25+39+56}{2}$

$s=\frac{120}{2}=60m$

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

$=\sqrt{60(60-25)(60-39)(60-56)}$

$=\sqrt{60\left(35\right)\left(21\right)\left(4\right)}=\sqrt{176400}$

$=420m^2$

$Areaoftriangle=\frac{1}{2}bh$, where b-base and h-height

$base=greatestside=56m$

$420=\frac{1}{2}\left(56\right)h$

$h=\frac{840}{56}$

$h=15m$