A rhombus-shaped sheet with perimeter 40cm and one diagonal 12cm, is painted on both sides at the rate of 5 percm2. Find the cost of painting.

Question

A rhombus-shaped sheet with perimeter 40cm and one diagonal 12cm, is painted on both sides at the rate of 5 percm2. Find the cost of painting.

Filo · Accepted Answer

Consider ABCD as the rhombus shaped sheet
It is given that the perimeter = 40cm
It can be written as
4 (side) = 40cm
So we get
Side = 10cm
We get
AB = BC = CD = AD = 10cm
Consider the diagonal AC = 12cm
We know that the diagonals of a rhombus bisect each other at right angles
So we get
AO = OC = 6cm
Consider

Δ

AOD
Using the Pythagoras theorem

A D^{2} = O D^{2} + A O^{2}

By substituting the values

1 0^{2} = O D^{2} + 6^{2}

On further calculation

O D^{2} = 100 - 36

By subtraction

O D^{2} = 64

By taking out the square root

O D = 64

So we get
OD = 8cm
We know that
BD = 2OD
So we get
BD = 2(8)
BD = 16cm
We know that
Area of rhombus ABCD =

\frac{1}{2}

(Product of diagonals)
It can be written as
Area of rhombus ABCD =

\frac{1}{2} \times A C \times B D

By substituting the values
Area of rhombus ABCD =

\frac{1}{2} \times 12 \times 16

By multiplication
Area of rhombus ABCD =

96 c m^{2}

It is given that the cost of painting is

₹5

per

c m^{2}

So the cost of paining both sides of rhombus =

₹5 \times (96 + 96)

We get
The cost of painting both sides of rhombus =

₹5 \times 192 = ₹960

Therefore, the cost of painting is

₹960.

Question Text	A rhombus-shaped sheet with perimeter 40cm and one diagonal 12cm, is painted on both sides at the rate of $5$ per $c m^{2}$ . Find the cost of painting.
Answer Type	Text solution:1
Upvotes	150

A rhombus-shaped sheet with perimeter 40cm and one diagonal 12cm, is painted on both sides at the rate of $5$ per $c m^{2}$ . Find the cost of painting.

Text solutionVerified

Practice questions from similar books