Question

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

• A. ₹ 878
• B. ₹ 887
• C. ₹ 918
• D. ₹ 981

Answer 1

The correct option is C ₹ 918

Let sides of a triangle be a = 51 m, b = 37 m and c = 20 m.
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 $m^2$ = ₹ 3
$\therefore \text{The cost of leveling per}306m^2=3\times 306=₹918$