Question

The sides of a triangular field are in the ratio of 3:5:7 and its perimeter is
300m. Find the cost ploughing the field at the rate of ₹.500 per 2
.
(Take √=1.73)

Answer 1

Answer:

₹12,97,500

Step-by-step explanation:

ratio of the sides of a triangle is 3:5:7

let the proportion be x,

=> the perimeter = 3x+5x+7x = 300m

                => 15x = 300m

                =>     x = 300/15 m

                =>     x = 20 m

=> sides of the trianlge 3x=3*20m , 5x=5*20m, 7x=7*20m

=> 60m, 100m, 140m

area of the scalene triangle = $\sqrt{s(s-a)(s-b)(s-c)}$ where s = $\frac{a+b+c}{2}$

here, s = (60+100+140)/2 = 300/2 = 150

=> Area, A = $\sqrt{150(150-60)(150-100)(150-140)}$m²

                 = $\sqrt{150(90)(50)(10)}$m²

                 = $\sqrt{3*50(3*3*10)(50)(10)}$m²

                 = 50*3*10$\sqrt{3}$m²

                 = 1500$\sqrt{3}$ = 1500*1.73 = 2595m²

Given that cost of ploughing = ₹500 / m²

therefore, cost of ploughing 2595m² = 2595 * ₹500

                                                              = ₹12,97,500