Question

Find the area of a triangle field of sides $18$, $24$m and $30$m. Also find the altitude corresponding to the shortest side.

Answer 1

The corresponding of the triangle is $18m,24m30m$

so, $A=18m,B=24m,C=30m$

By using herons formula we

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

$S=\frac{18+24+30}{2}=\frac{72}{2}=36$

$AREA=\sqrt{S(S-A)(S-B)(S-C)}$

$AREA=\sqrt{36(36-18)(36-24)(36-30)}$

$AREA=\sqrt{36\left(18\right)\left(12\right)\left(6\right)}$

$AREA=\sqrt{46656}$

$AREA=216m^2$

Let altitude is Hm

AREA of triangle is also written as=$\frac{1}{2}\times b\times$h

$216=\frac{1}{2}\times 18\times h$

$h=\frac{216\times 2}{18}=24m$