Question

A rhombus sheet whose perimeter is 30m and whose one diagonal is 10m long is painted on both sides at the rate of Rs5per m sq find the cost of painting.

Answer 1

Answer:

The cost of Painting the Rhombus Sheet is Rs.559

Step-by-step explanation:

The perimeter of rhombus = 4*side

so,

4*side = 30

or,

side is equal to 30/4 = 7.5 m

diagonal of the rhombus is equal to 10 m

now,

• The digonal of a rhombus divides it into two congruent triangles eaual in area.

now,

considering one triangle:-

• side 1 = 7.5 m

• side 2= 7.5 m

• side 3 = 10 m

applying the herons formula to find the area of the triangle:-

s= [a+b+c]/2 = [7.5+7.5+10]/2 = 25/2

applying Heron's Formula:-

$A=\sqrt{s[s-a][s-b][s-c]} \\\\A=\sqrt{\frac{25}{2}[\frac{25}{2}-7.5][\frac{25}{2}-7.5][\frac{25}{2}-10] } \\\\A=\frac{25}{2}-7.5\sqrt{\frac{25}{2}[2.5]} \\\\A=5\sqrt{\frac{25*25}{20} }\\ \\A=5*25\sqrt{\frac{1}{2*2*5} } \\\\A=\frac{125}{2}*\frac{\sqrt{5} }{5}  \\\\A=12.5\sqrt{5} \\\\A= 12.5*2.236 =27.95 m^{2}$

so,

The area of Rhombus is equal to 2*area of triangle.

so

• Area of Rhombus = 2* 27.95 = 55.9 sq.m

now,

• The cost of painting the sheet is equal to 5*55.9 = Rs.279.50

Now ,

The sheet is painted on both the sides.

so,

Total cost of painting is equal to 2*279.5 = Rs.559

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