The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per m² is Rs 918. Is the given statement true or false and justify your answer.
Solution:
Given, the ground in the form of a triangle
The sides are 51 m, 37 m and 20 m.
The cost of levelling the ground at the rate of Rs. 3/m² is Rs. 918.
We have to determine if the given statement is true or false.
Let a = 51 m
b = 37 m
c = 20 m
By Heron’s formula,
Area of triangle = √s(s - a)(s - b)(s - c)
Where s= semiperimeter
s = (a + b + c)/2
So, s = (51 + 37 + 20)/2
= 108/2
s = 54 m
Now, area = √54(54 - 51)(54 - 37)(54 - 20)
= √54(3)(17)(34)
= √9 × 6 × 3 × 17 × 17 × 2
= √9 × 3 × 3 × 2 × 2 × 17 × 17
= 3 × 3 × 2 × 17
= 18 × 17
Area = 306 m²
Cost of leveling 1 m² = Rs. 3
Cost of leveling entire area = 306 × 3
Cost of leveling the ground = Rs. 918
Therefore, the given statement is true.
✦ Try This: Write True or False and justify your answer: The cost of levelling the ground in the form of a triangle having the sides 31 m, 17 m and 23 m at the rate of Rs2.53 per m² is Rs 818.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12
NCERT Exemplar Class 9 Maths Exercise 12.2 Problem 8
The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per m² is Rs 918. Is the given statement true or false and justify your answer.
Summary:
The given statement “The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per m² is Rs 918” is true
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