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# 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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