Question

The edges of a triangular board are 6 cm, 8 cm and 10 cm long. The cost of painting it at the rate of 9 paise per cm² is
(a) ₹ 2
(b) ₹ 2.16
(c) ₹ 2.48
(d) ₹ 3

Answer 1

Given:
The edges of a triangular board are 6 cm, 8 cm and 10 cm long.
The cost of painting per cm² is 9 paise.


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, $s=\frac{6+8+10}{2}=\frac{24}{2}=12$

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{12\left(12-6\right)\left(12-8\right)\left(12-10\right)} \\ =\sqrt{12\left(6\right)\left(4\right)\left(2\right)} \\ =\sqrt{\left(3\times 2\times 2\right)\left(3\times 2\right)\left(2\times 2\right)\left(2\right)} \\ =\left(3\times 2\times 2\times 2\right) \\ =24{\mathrm{cm}}^2 \end{gathered}$$

The cost of painting per cm² = 9 paise.
The cost of painting 24 cm² = 24 × 9 paise
= 216 paise
= ₹ 2.16


Hence, the correct option is (b).