Question

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

Answer 1

Given, Perimeter $=32m$

The length of a side $=\frac{32}{4}$$=$$8m$

Diagonal of a rhombus $=10m$

∴ Area $=$$\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

In Δ ABC, sides are $8m,8m,10m$
∴$s$$=$$\frac{a+b+c}{2}=\frac{8+8+10}{2}=\frac{26}{2}=13$
$$\begin{gathered} =\sqrt{13\left(13-8\right)\left(13-8\right)\left(13-10\right)} \\ =\sqrt{13\times 5\times 5\times 3} \\ =5\sqrt{39}{m}^2 \end{gathered}$$
∴ Area of one sides of sheet $=$$2\times 5\sqrt{39}{m}^2$
$=10\sqrt{39}{m}^2$
and area of both sides of sheet $=$ $2\times 10\sqrt{39}{m}^2$
$$\begin{gathered} =20\sqrt{39}{m}^2 \\ =20\times 6.25m^2 \\ =125m^2 \end{gathered}$$
Rate of polishing the both sides of the sheet $=₹5$ per $m^2$

Therefore, total cost of painting$=$$125\times 5=₹625$.