Question

Find the area of the triangle whose sides are 50 m, 78 m and 112 m and also find the length of the perpendicular from the opposite vertex to the side of length 112 m.

Answer 1

Given:-

$a=50m$

$b=78m$

$c=112m$

As we know that, perimeter is given as-

$s=\frac{a+b+c}{2}$

$\Rightarrow s=\frac{50+78+112}{2}=120$

According to Heron's formula,

Area of $△=\sqrt{s(s-a)(s-b)(s-c)}$

$\Rightarrow$ Area of $△=\sqrt{120\times (120-50)\times (120-78)\times (120-112)}=1680m^2$

We know that,

Area of $△=\frac{1}{2}\times$ Base $\times$ Perpendicular

$\Rightarrow 1680=\frac{1}{2}\times 112\times$ Perpendicular

$\Rightarrow$ Perpendicular $=\frac{1680\times 2}{112}=30m$

Thus the length of perimeter is $30m$.

Hence the correct answer is $30m$.