Question

A triangular wall having sides 3 m, 5 m and 6 m has to be painted. If the cost of painting $1m^2$ of a wall is ₹5, what is the cost of painting the whole wall?

• A. ₹$16\sqrt{13}$
• B. ₹$10\sqrt{14}$
• C. ₹$14\sqrt{10}$
• D. ₹$14$

Answer 1

The correct option is B

₹$10\sqrt{14}$

Semi perimeter of a triangle = $\frac{(a+b+c)}{2}$ $\Rightarrow$ $\frac{(3+5+6)}{2}=7m$

Area of a triangle = $\sqrt{s(s-a)(s-b)(s-c)}$ $\Rightarrow$ $\sqrt{7(7-3)(7-5)(7-6)}$

$\Rightarrow$ $\sqrt{7\times 4\times 2\times 1}$
$\Rightarrow$ $\sqrt{14\times 4}$

$\Rightarrow \sqrt{56}=2\sqrt{14}{m}^2$

Since, cost of painting $1m^2$ of wall is ₹5,

The cost of painting the whole wall $=5\times 2\sqrt{14}=₹10\sqrt{14}.$