Question

A rhombus sheet, whose perimeter is 32 m and whose diagonal is 10 m long, is painted on both the sides at the rate of Rs 5 per m². Find the cost of painting.

Answer 1

Perimeter of a rhombus = 32 m 

We know, Perimeter of a rhombus = 4 x side 

 4 x side = 32 

side = a = 8 m 

Each side of rhombus is 8 m 

AC = 10 m (Given)

Then, OA = 1/2 x AC 

OA = 1/2 x 10 

OA = 5 m 

In right triangle AOB, 

From Pythagoras theorem; 

OB² = AB² – OA² 

= 8² – 5² 

= 64 – 25 

= 39 

OB = √39 m And, 

BD = 2 x OB

BD = 2√39 m 

Area of the sheet = 1/2 x BD x AC 

= 1/2 x (2√39 x 10) 

= 10√39 

Area of the sheet is 10√39 m² 

Therefore, cost of printing on both sides of the sheet, at the rate of Rs. 5 per m² 

= Rs. 2 x (10√39 x 5) 

= Rs. 625.