Question

A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm is painted on both sides of the rate of Rs 5 per meter sqaure.

Answer 1

Given:

The perimeter of the rhombus-shaped sheet = 40 cm

The length of one diagonal, d₁ = 12 cm

The rate of painting the rhombus sheet on both sides is Rs. 5 per square meter

To find:

The cost of painting

Solution:

Let's assume,

"a" → be the length of each side of the rhombus-shaped sheet.

"d₂" → be the length of another diagonal of the rhombus-shaped sheet

Finding the value of a:

Perimeter of rhombus = sum of all sides

given perimeter = 40 cm

$\implies 40 = a + a + a + a$

$\implies 40 = 4a$

$\implies a = \frac{40}{4}$

$\implies \bold{a = 10\: cm}$

Finding the value of d₂:

The formula to find the value of d₂ is given as,

$\boxed{\bold{d_2=\sqrt{4a^2 - d_1^2} }}$

By substituting the values of a = 10 cm and d₁ = 12 cm in the above formula,  

$d_2=\sqrt{4(10)^2 - (12)^2} }} = \sqrt{400 - 144} }} = \sqrt{256} }} = 16 \: cm$

Finding the area of the rhombus-shaped sheet:

Area of rhombus = ½ × d₁ × d₂ = ½ × 12 × 16 = 6 × 16 = 96 cm²

We have to convert cm² to m² because the rate of cost is given in m²

If 1 cm² = $\frac{1}{10000}$ m²

Then 96 cm² = $\frac{96}{10000}$ m² = 0.0096 m²

Finding the total cost of painting:

If the cost of painting the sheet of 1 m² = Rs. 5

Then the cost of painting the sheet of 0.0096 m² is,

= Rs. 5 × 0.0096 m²

= Rs. 0.048

Now,

The cost of painting the sheet on both sides = Rs. 0.048 × 2 = Rs. 0.096

Thus, the cost of painting the rhombus-shaped sheet on both sides is Rs. 0.096.

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Answer 2

Step-by-step explanation:

Let ABCD be a rhombus, then AB=BC=CD=DA=x

Perimeter of rhombus =40cm

⇒4x=40cm⇒x=10cm

∴AB=BC=CD=DA=10cm

In △ABC,S=

2

a+b+c

=

2

10+10+12

=16cm

ar△ABC=

16(16−10)(16−10)(16−12)

=

16×6×6×4

=48cm

2

ar.ABCD=2×48=96cm

2

Cost of painting the sheet =Rs(5×96×2)=Rs960 [Both sides]