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?
(Take $\sqrt{14}$ = 3.742)

Answer 1

Semi perimeter of a triangle = s
= $\frac{Perimeter}{2}=\frac{a+b+c}{2}=\frac{3+5+6}{2}=7m$
Area of a triangle $=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{7(7-3)(7-5)(7-6)}=\sqrt{7\times 4\times 2\times 1}=2\sqrt{14}{m}^2$
Since, cost of painting 1 $m^2$ of wall is ₹ 5,
The cost of painting the whole wall = $5\times 2\sqrt{14}=₹10\sqrt{14}=₹10\times 3.742=₹37.42$