The sides of a triangular field are 41 m, 40 m and 9 m. Find the number of rose beds that can be prepared in the field, if each rose bed, on an average needs 900 cm² space.
Solution:
Given, the sides of a triangular field are 41 m, 40 m and 9 m.
Each rose bed needs an average of 900 cm² space
We have to find the number of rose beds that can be prepared in the field.
By Heron’s formula,
Area of triangle = √s(s - a)(s - b)(s - c)
Where s= semiperimeter
s = (a + b + c)/2
So, s = (41 + 40 + 9)/2
= 90/2
s = 45 m
Now, area = √[45(45 - 41)(45 - 40)(45 - 9)]
= √[45 × 4 × 5 × 36]
= √[9 × 5 × 5 × 4 × 4 × 9]
= 9 × 5 × 4
= 180 m²
We know, 1 m = 100 cm
1 cm = 1/100 m
i.e., 1 cm = 0.01 m
Similarly, 900 cm² = 0.09 m²
Area needed for one rose bed = 0.09 m²
Number of rose beds = entire area of triangular field / area needed for one rose bed
= 180/0.09
= 2000
Therefore, the number of rose beds is 2000.
✦ Try This: The sides of a right triangular field are in the ratio 5:3:4 and its perimeter is 180 m. Find the cost of levelling the field at the rate of Rs.10 per square metre.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12
NCERT Exemplar Class 9 Maths Exercise 12.3 Sample Problem 1
The sides of a triangular field are 41 m, 40 m and 9 m. Find the number of rose beds that can be prepared in the field, if each rose bed, on an average needs 900 cm² space.
Summary:
The sides of a triangular field are 41 m, 40 m and 9 m. The number of rose beds that can be prepared in the field, if each rose bed, on an average needs 900 cm² space is 2000
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