Question

sides of a triangular field are 5m, 7m and 8m. find the
cost of levelling the field at the sake of rupees10 þer m²?​

Answer 1

Answer:

₹173. 2

Step-by-step explanation:

Given -

Sides of a triangular field = 5m, 7m and 8m

The rate of leveling the field = ₹10

To find -

The cost of leveling the field.

Solution -

To find the cost first we have to find out the area of field.

Area of Triangle =

$\sqrt{s(s - a)(s - b)(s - c)}$

Here,

s = semi perimeter

a, b and c are three sides of triangle

We have sides now we have to find the semi-perimeter

$s = \frac{(a + b + c)}{2} \\ = \frac{(5 + 7 + 8)}{2} m \\ = \frac{20}{2} m \\ = 10m$

Now area

$a = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{10 \times (10 - 5)(10 - 7)(10 - 8)} \\ = \sqrt{10 \times 5 \times 3 \times 2} \\ = \sqrt{5 \times 2 \times 5 \times 3 \times } 2 \\ = \sqrt{5 \times 5 \times 2 \times 2 \times 3} \\ = \sqrt{ {5}^{2} \times {2}^{2} \times 3 } \\ = 5 \times 2 \sqrt{3} \\ = 10 \sqrt{3} {m}^{2}$

Hence the area = 10√3 m²

= 10 × 1.732 m²

= 17.32 m² (approx)

Cost of leveling 1 m² = ₹10

Cost of leveling 17.32 m² = ₹10 × 17.32

= ₹173.2

Cost of leveling the field = ₹173.2

Hope it helps.