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 ₹ 3 per m² is __________.

Answer 1

Given:
A ground is in the form of a triangle having sides 51 m, 37 m and 20 m.
The cost of levelling the ground per m² is ₹ 3.


Using Heron's formula:
If a, b and c are three sides of a triangle, then
area of the triangle = $\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$ , where $s=\frac{a+b+c}{2}$.


Here, $s=\frac{51+37+20}{2}=\frac{108}{2}=54$

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{54\left(54-51\right)\left(54-37\right)\left(54-20\right)} \\ =\sqrt{54\left(3\right)\left(17\right)\left(34\right)} \\ =\sqrt{\left(2\times 3\times 3\times 3\right)\left(3\right)\left(17\right)\left(2\times 17\right)} \\ =\left(3\times 3\times 2\times 17\right) \\ =306{\mathrm{m}}^2 \end{gathered}$$

The cost of painting per m² = ₹ 3
The cost of painting 306 m² = ₹ 306 × 3
= ₹ 918

Hence, the cost of levelling the ground at the rate of ₹ 3 per m² is ₹ 918.