Question

How much will it cost to have a triangular field weeded at the rate of Rs 2 per square metre if the length of the field's sides are 11 m, 61 m and 60 m?

Answer 1

Lengths of the sides of the triangle are 11 m, 61 m and 60 m.
Semi-perimeter of a triangle = $s=\frac{a+b+c}{2}$
Semi-perimeter$=\frac{11+61+60}{2}=66\mathrm{cm}$
Area of a triangle$=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$
$$\begin{gathered} =\sqrt{66\left(66-11\right)\left(66-61\right)\left(66-60\right)} \\ =\sqrt{66\left(55\right)\left(5\right)\left(6\right)} \\ =\sqrt{108900} \\ =330 \end{gathered}$$
Area of the triangle is 330 sq m.
Cost per square metre = Rs 2
Cost of weeding the triangular field = (area of the triangle) × (cost per square metre)
= Rs 330 × 2
∴ Cost of weeding the triangular field = Rs 660 .