A rhombus shaped sheet whose perimeter is 32cm and one of the diagonal is 10cm long painted on both the sides at the rate of rs5 per Sam.find the cost of painting.
All four sides are equal, so each side of the rhombus is 8 cm
get angle Ø , opposite the 10 cm diagonal
10^2 = 8^2 + 8^2 - 2(8)(8)cosØ
cosØ = 7/32, then sinØ = 5√39/32
area = 8(8)sinØ
= ...
you take over
deepanshu your answer is madarchod bhosadi ka
To find the cost of painting the rhombus-shaped sheet, we need to calculate its area first.
First, let's find the length of the sides of the rhombus.
Since a rhombus has equal sides, we divide the perimeter by 4:
32 cm ÷ 4 = 8 cm
So, each side of the rhombus is 8 cm long.
Next, let's find the area of the rhombus.
The area of a rhombus can be calculated by multiplying the lengths of its diagonals and dividing by 2:
Area = (diagonal1 * diagonal2) / 2
Given that one of the diagonals is 10 cm, let's find the other diagonal.
Using the properties of a rhombus, we know that the diagonals are perpendicular bisectors of each other and divide the rhombus into four congruent right-angled triangles.
Let's consider one of these triangles. The hypotenuse of the triangle is one of the sides of the rhombus, which we already calculated to be 8 cm. And one of the legs is half the length of the other diagonal (let's call it d).
Using Pythagoras theorem:
(8/2)^2 + (d/2)^2 = 8^2
4^2 + (d/2)^2 = 64
16 + (d/2)^2 = 64
(d/2)^2 = 64 - 16
(d/2)^2 = 48
d/2 = √48
d/2 = 4√3
d = 8√3 cm
Now, let's calculate the area of the rhombus:
Area = (10 cm * 8√3 cm) / 2
Area = 40√3 cm^2
Finally, let's calculate the cost of painting both sides of the rhombus.
Since the cost is given as rs5 per square cm, let's multiply the area by rs5:
Cost = 40√3 cm^2 * rs5/cm^2
Cost = 200√3 rs
Therefore, the cost of painting both sides of the rhombus-shaped sheet is 200√3 rs.