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.