Question

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

Answer 1

perimeter = 4 a = 32 => side = 8m
diagonal c = 10m    to find other diagonal d.      Then area = c d / 2
cost of painting both sides = 2 * (c d / 2) * 5   Rs

In a Rhombus,    c² + d² = 4 a²           and                c² - d² = 4a² cos Ф
                    so d² = 4 * 8² - 10²  = 156      d = 2 √39  m
Cost = 100 √39  Rs.

Answer 2

here is your answer

Perimeter of a rhombus = 32 m

We know ,

Perimeter of rhombus = 4 × side

so 49 = 32m

so a = 8 m

suppose AC = 10 = OA = 1/2 AC

= 1/2 × 10

= 5 m

In a Rhombus,    c² + d² = 4 a²          

           c² - d² = 4a² cos Ф
                 
   then d² = 4 * 8² - 10²  = 156     

d = 2 √39  m

Cost = 100 √39  answer