A field is in the shape of parallelogram, whose adjacent sides are 120 m and 170 m. If its one diagonal is 250 m, then cost of ploughing the field at ₹20 per sq m is :

1. ₹ 90,000

2. ₹ 1,20,000

3. ₹ 1,80,000

4. ₹ 3,60,000

Let ABCD be a field in the shape of a || gm .

Calculating area of triangle BCD,

CD = a = 120 m, BC = b = 170 m, BD = c = 250 m

$\text{Semi-perimeter (s)} = \dfrac{a + b + c}{2} \\[1em] = \dfrac{120 + 170 + 250}{2} \\[1em] = \dfrac{540}{2} \\[1em] = 270 \text{ m.}$

By formula,

$\Rightarrow \text{Area of triangle} = \sqrt{s(s - a) (s - b) (s - c)} \\[1em] \Rightarrow \text{Area of triangle BCD} = \sqrt{270(270 - 120) (270 - 170) (270 - 250)} \\[1em] = \sqrt{270(150) (100) (20)} \\[1em] = \sqrt{81000000} \\[1em] = 9000 \text{ m}^2.$

We know that,

In a parallelogram, the diagonal divides the parallelogram into two congruent triangles.

Thus, area of triangle ABD = area of triangle BCD = 9000 m².

Area of parallelogram ABCD = Area of triangle ABD + Area of triangle BCD

= 9000 + 9000 = 18000 m².

Given,

Cost of ploughing the field = ₹20 per sq m.

Total cost = Area × Cost per sq m = 18000 × ₹20 = ₹3,60,000.

Hence, option 4 is the correct option.