Question

a rhombus sheet whose perimeter is 140m and whose ine diagonal is 56m long,is painted o n bothsides at the rate of ₹5/m^2.find the cost of painting​
WITH STEP BY STEP EXPLAINATION PLZ​

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