The cost of levelling 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 m2 is Rs. 918.
True
Let sides of a triangle be $a=51 \mathrm{~m} b=37$ mand $c=20 \mathrm{~m}$ Now, semi-perimeter of triangle,
$s=\frac{a+b+c}{2}=\frac{51+37+20}{2}=\frac{108}{2}=54 \mathrm{~m}$
$\therefore \quad$ Area of a triangle $=\sqrt{s(s-a)(s-b)(s-c)}$ [by Heron's formula]
$=\sqrt{54(54-51)(54-37)(54-20)}$
$=\sqrt{54 \times 3 \times 17 \times 34}$
$=\sqrt{9 \times 3 \times 2 \times 3 \times 17 \times 17 \times 2}$
$=3 \times 3 \times 2 \times 17=306 \mathrm{~m}^{2}$
$\because$ Cost of levelling per $m^{2}=₹ 3$
$\therefore$ Cost of levelling per $306 \mathrm{~m}^{2}=3 \times 306=₹ 918$
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