Question

find the cost of ploughing a field at the rate of ₹20 per sq m if dimensions of the triangular plot area 120 m, 160m and 200m​

Answer 1

given:-

dimensions of the triangular field 120m, 160m and 200m

here we have to find the cost of ploughing it @ 20 rupees per m²

so first of all, we have to find it's area.

let the sides be a, b and c respectively.

semi-perimeter = (120 + 160 + 200)/2

= 480/2

= 240m

using heron's formula = √s(s - a)(s - b)(s - c)

= √[240(240 - 120)(240 - 160)(240 - 200)]

= √(240 × 120 × 80 × 40)

= √(2 × 2 × 2 × 2 × 3 × 5 × 2 × 2 × 2 × 3 × 5 × 2 × 2 × 2 × 2 × 5 × 2 × 2 × 2 × 5)

= √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5 × 5)

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5

= 9600m²

the area of the triangular field is 9600m²

hence total cost @ rupees 20 per m² = 20 × 9600

= rupees 192000

Answer 2

Answer :- 9600m²

Sides :-

120m

160m

200m

S (semiperimeter) = 120+160+200/2

480/2

240 m

Using Herons Formula

√(240×120×80×40)

By solving it we have

2×2×2×2×2×2×2×2×3×5×5

= 9600m²