A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
Solution:
We will divide the given rhombus into two triangles, and by using Heron’s formula, we can calculate the area of triangles.
Heron formula for the area of a triangle = √s(s - a)(s - b)(s - c)
Where a, b and c are the sides of the triangle, and s = Semi-perimeter = Half the Perimeter of the triangle = (a + b + c)/2
Let the longer diagonal AC divides the rhombus ABCD into two congruent triangles.
For ∆ABC, a = b = 30 m, c = 48 m
And Semi Perimeter(s) = (a + b + c)/2
s = (30 + 30 + 48)/2
s = 108/2
s = 54 m
By using Heron’s formula,
Area of ΔABC = √s(s - a)(s - b)(s - c)
= √54(54 - 30)(54 - 30)(54 - 48)
= √54 × 24 × 24 × 6
Area of ΔABC = 432 m2
Area of rhombus = 2 × Area of a ΔABC
= 2 × 432 m2
= 864 m2
Since, number of cows = 18
The area of grass field will each cow get = (Total area of the rhombus) / 18
= 864 m2/18
= 48 m2
Thus, each cow will be getting a 48 m2 area of the grass field.
☛ Check: NCERT Solutions Class 9 Maths Chapter 12
Video Solution:
A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
Class 9 Maths NCERT Solutions Chapter 12 Exercise 12.2 Question 5
Summary:
It is given that rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, we have found that each cow would be getting an area of 48 m² to graze.
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