Question

The edges of a triangular board are $6cm,8cm$ and $10cm$. The cost of painting it at the rate of $9$ paise per $c{m}^2$ is:

• A. $Rs.2.00$
• B. $Rs.3.00$
• C. $Rs.2.16$
• D. $Rs.2.48$

Answer 1

The correct option is C $Rs.2.16$

Let $a=6cm$, $b=8cm$, $c=10cm$.

$s=\frac{a+b+c}{2}$

$\Rightarrow s=\frac{6+8+10}{2}$

$\Rightarrow s=12cm$

Now, area of triangular board:

$△=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{12(12-6)(12-8)(12-10)}$

$=\sqrt{12\times 6\times 4\times 2}$

$=\sqrt{4\times 3\times 3\times 2\times 4\times 2}$

$=2\times 3\times 4$

$=24c{m}^2$

Now, cost of painting $1c{m}^2$ $=9$ $paise$ $Rs.0.09$

$\therefore$Cost of painting $24c{m}^2$

$\Rightarrow 24\times 0.09=Rs.2.16$