Question

A gardener has to put fence all around a triangular field with sides 120 m, 80 m and 60

m. In the middle of each of the sides, there is a gate of width10 m.

(i) Find the length of wire needed for fencing.

(ii) Find the cost of fencing at the rate of 6 per metre.

(iii) Find the area of triangular field​

Answer 1

Answer:

120+80+60=260m

so 260m wire he needs for fencing

6x260=1560rupees

so he needs to spend 1560 rupees for fencing

120x80x60=576000

so its area is 576000m²

Answer 2

The length of the wire needed for the fence is 460 m.

Given : A gardener has to put a double fence all around a triangular path with sides 120m, 80m and 60m.

In the middle of each side there is a gate of width 10m.

The perimeter of triangle = Sum of all sides

= 120+80+60 = 260 m

Now , the length of wire needed for fence =  2 x [Perimeter of triangle - 3(10)]

= 2 x(260-30) = 2 x (230) = 460 m

Therefore , the length of the wire needed for the fence is 460 m .

Cost of fencing at the rate= Rs.6 per metre

                                           = 6×460

Cost of fencing at the rate = 2,760

Area of triangular field​ = A=√s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c/2

Solving for A

A= 1/4√-a⁴+ 2(a b)²+2(ac)²﹣b⁴+2(bc)²﹣c⁴

  = 1/4√﹣120⁴+2·(120·80)²+2·(120·60)²﹣80⁴+2·(80·60)²﹣60⁴

  = 2133.0729m²