Find the cost of levelling a ground in the form of a triangle having the sides 22 m, 28 m and 30 m at the rate of ₹ 3 per m2. ₹ 883.82₹ 881.82₹ 882.82₹ 884.82
Answers
Given,
The length of the three sides of the given triangular ground are 22 metres, 28 metres and 30 metres.
Cost rate of levelling is ₹3 per square metre.
To find,
The total cost of ground levelling.
Solution,
The perimeter of the triangle = (22+28+30) = 80 metres
The half perimeter of the triangle = 80/2 = 40 metres
The area of the triangle (half perimeter formula or Heron's formula) = ✓[40×(40-22)(40-28)(40-30)] = ✓(40×18×12×10) = ✓86400 = 294 m² (approx)
Now,
Cost for 1m² = ₹ 3
Cost for 294 m² = 3×294 = ₹ 882
Hence,the total cost of ground levelling is approximately ₹882
Given : a ground in the form of a triangle having the sides 22 m, 28 m and 30 m is levelled at the rate of ₹ 3 per m²
To find : cost of levelling ground
Solution:
Sides of triangel
22 , 28 , 30
s = (22 + 28 + 30)/2 = 80/2 = 40
Area of triangle using Heron formula
A = √s(s -a)(s-b)(s-c)
= √40(40-22)(40-28)(40-30)
= √40*18*12*10
= √10 * 2 * 2 * 6 *3 * 6 * 2 * 10
= 10 * 2 * 6 √6
= 120√6 m²
cost of levelling per m² = Rs 3
Cost of levelling the ground = 120√6 * 3
= 360√6 Rs
= 360 * 2.4495
= 881.82
cost of levelling ground = Rs 881.82
₹ 881.82 is correct option
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