Question

A ground is in the form of a triangle having sides 51 m, 37 m and 20 m. The cost of levelling the ground at the rate of Rs. 3 per $m^2$ is

Answer 1

Given: Sides of triangle be a = 51 m, b = 37 m, and c = 20 m
If s be the perimeter of triangle, then
$s=\frac{a+b+c}{2}=\frac{51+37+20}{2}=\frac{108}{2}=54m$

$\text{Area of triangle}=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{54(54-51)(54-37)(54-20)}$
$=\sqrt{54\times 3\times 17\times 34}$
$=\sqrt{9\times 3\times 2\times 3\times 17\times 17\times 2}$
$=3\times 2\times 17$
$=306m^2$
As, cost of levelling per $m^2=Rs3$
$\therefore \text{Cost of levelling}306m^2\text{of area}=3\times 306$
= Rs 918
Hence, the required cost is Rs 918.