Question

A Rhombus shaped sheet with perimeter $40$cm and one diagonal $12$ cm is pointed on both sides at the rate of Rs. $5per{m}^2$. Find the cost of painting.

Answer 1

Let $ABCD$ be a rhombus, then $AB=BC=CD=DA=x$

Perimeter of rhombus $=40cm$

$\Rightarrow 4x=40cm\Rightarrow x=10cm$

$\therefore AB=BC=CD=DA=10cm$

In $△ABC,S=\frac{a+b+c}{2}=\frac{10+10+12}{2}=16cm$

$ar△ABC=\sqrt{16(16-10)(16-10)(16-12)}=\sqrt{16\times 6\times 6\times 4}=48c{m}^{2}ar.ABCD=2\times 48=96c{m}^2$

Cost of painting the sheet $=Rs(5\times 96\times 2)=Rs960$ [Both sides]