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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