Question

a rhombus shaped sheet has the perimeter of 52 cm and one diagnal 10cm, is painted on both sides at the rate of 7$ find the cost of the painting​

Answer 1

Given :

• A rhombus - shaped sheet with perimeter 52 cm and one diagonal 10 cm is painted on both sides at the rate of Rs.7.

To find :

• The cost of painting.

solution :

We know that ,

• all sides of rhombus are equal length.

Let the ABCD be a rhombus each side be r

We have ,

• ►Perimeter of rhombus=52cm

• ►One diagonal of rhombus(d¹)=10cm

• ►Rate=Rs.7

According to Question

$: \implies\tt{52=4\times r}$

$: \implies\sf{r=\cancel{\dfrac{52}{4} }}$

$:\implies\sf{r\:=\:13\:cm}$

We get In△ABC ,

• ►a=AB=13cm
• ►b=BC=13cm
• ►c=AC=10cm

$: \implies\tt{Semi-perimeter\:(S)=\dfrac{a+b+c}{2} }\\\\\\: \implies\tt{Semi-perimeter=\dfrac{13+13+10}{2} }\\\\\\: \implies\tt{Sem-perimeter=\cancel{\dfrac{36}{2} }}\\\\\\: \implies\tt{Semi-perimeter=18\:cm}$

Now,

$: \implies\tt{Area\:of\:\triangle ABC=\sqrt{s(s-a)(s-b)(s-c)} }\\\\\\: \implies\tt{Area\:of\:\triangle ABC=\sqrt{18(18-13)(18-13)(18-10)}} \\\\\\: \implies\tt{Area\:of\:\triangle ABC=\sqrt{18(5)(5)(8) } \:cm^{2} }\\\\\\: \implies\tt{Ara\:of\:\triangle ABC=\sqrt{3600} \:cm^{2}} \\\\\\: \implies\tt{Area\:of\:\triangle ABC=60\:cm^{2} }$

∴Area of rhombus = 2(Area of ΔABC)

➻ Area = 2(60)cm²

➻ Area = 120 cm²

• Cost of painting of sheetbof 1cm ² =Rs.7

• Cost of painting.of sheet of 120cm ² =Rs.(7×120)=Rs.840

∴ The both sides is painted = Rs.2(840) = Rs.1680