Question

Question 8
Write True or False and justify your answer:

The cost of leveling the ground in the form of a triangle having the sides 51m, 37m and 20m at the rate of Rs.3 per $m^2$ is Rs.918.

Answer 1

True
Let sides of a triangle be a = 51m, b = 37m and c = 20m.
Now, semi-perimeter of triangle,
$s=\frac{a+b+c}{2}=\frac{51+37+20}{2}=\frac{108}{2}=54m$
$\therefore$ Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$ [by Heron’s formula]
$=\sqrt{54(54-51)(54-37)(54-20)}$
$=\sqrt{54\times 3\times 17\times 34}$
$=\sqrt{9\times 3\times 2\times 3\times 17\times 17\times 2}$
$=3\times 3\times 2\times 17=306m^2$
Given that the cost of leveling per $m^2$ = Rs.3
$\therefore$ The cost of leveling per 306 $m^2=3\times 306=Rs.918$