Question

A rhombus sheet whose perimeter = 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs. 5 per $m^2$. Find the cost of painting.

Answer 1

Perimeter of the rhombus shaped sheet
= 32 m

$\therefore$ Length of each side = $\frac{32}{4}=8m$
and length of one diagonal AC= 10 m
In $\Delta$ ABC, sides are 8m, 8m, 10m
$\therefore s=\frac{a+b+c}{2}=\frac{8+8+10}{2}=\frac{26}{2}=13$
$\therefore$ Area = $\sqrt{s(s-a)(s-b)(s-c)}$
= $\sqrt{13(13-8)(13-8)(13-10)}$
= $\sqrt{13\times 5\times 5\times 3}{m}^2$
= $5\sqrt{39}{m}^2$
$\therefore$ Area of one sides of sheet = $2\times 5\sqrt{39}{m}^2$
= $10\sqrt{39}{m}^2$
and area of both sides of sheet = $2\times 10\sqrt{39}{m}^2$
= $20\sqrt{39}{m}^2$
=$20\times 6.25m^2=125.0m^2$
Rate of polishing the both sides of sheet
= Rs. 5 per $m^2$

$\therefore$ Total cost = 125.0 $\times$ Rs.5 = Rs. 625