# A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m². Find the cost of painting.

**Solution:**

Given, a sheet in the shape of rhombus with perimeter 40 cm

One diagonal is 12 cm

We have to find the cost of painting both the sides at the rate of Rs. 5 per cm²

Let ABCD be a rhombus with each side equal to x cm

AB = BC = CD = AD = x cm

Perimeter of rhombus = 40

AB + BC + CD + AD = 40

x + x + x + x = 40

4x = 40

x = 40/4

x = 10

Therefore, the length of each side of rhombus is 10 cm

In triangle ABC,

AB = BC = 10 cm

AC = 12 cm

Since two sides are equal the triangle is an isosceles triangle.

Area of isosceles triangle = a/4 √4b²-a²

Where, a = base

b = equal side

Here, a = 12 cm and b = 10 cm

Area = 12/4 √4(10)² - (12)²

= 3√4(100) - 144

= 3√400 - 144

= 3√256

= 3(16)

Area of triangle ABC = 48 cm²

Area of rhombus = 2 × area of triangle ABC

= 2(48)

Area of rhombus = 96 cm²

Cost of painting 1 m² = Rs. 5

Cost of painting one sheet = 96 × 5

= Rs. 480

Cost of painting sheet on both sides = 2 × 480

= Rs. 960

Therefore, the cost of painting is Rs. 960/-

**✦ Try This: **A rhombus shaped sheet with perimeter 60 cm and one diagonal 21 cm, is painted on both sides at the rate of Rs 6 per m². Find the cost of painting.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 12

**NCERT Exemplar Class 9 Maths Exercise 12.3 Problem 9**

## A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m². Find the cost of painting.

**Summary:**

A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m². The cost of painting is Rs. 960/-

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