Question

10 mthe ghost the cost of c u l t i v a t i n g a r a triangular field ​

Answer 1

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Correct Question :-

The cost of turfing a triangular field at the rate of Rs. 5 per sq.m is Rs. 1350 .If the sides of the field are in the ratio of 5:12:13. Find the sides of field .

Solution :-

Given :-

Cost of turfing a triangular field @ Rupees 5 per m² is rupees 1350.

Therefore area of the triangular field = 1350/5

= 270m²

Now,

Ratio between the sides of the triangular field is given 5 : 12 : 13

Let the sides of the triangular field be 5x, 12x and 13x respectively.

➡ Semi-perimeter of the triangle = (5x + 12x + 13x)/2

= 15x

By using heron's formula, we get

√s(s - a)(s - b)(s - c) = area of the triangle where s is the semi-perimeter and a, b and c are it's sides respectively.

➡ √[15x(15x - 5x)(15x - 12x)(15x - 13x)] = 270m²

➡ √(15x × 10x × 3x × 2x) = 270m²

➡ √(900x⁴) = 270m²

➡ 30x² = 270m²

➡ x² = 270/30

➡ x² = 9

➡ x = √9

➡ x = 3

Hence, the sides of the triangular field are :-

5x = 5 × 3 = 15m

12x = 12 × 3 = 36m

13x = 13 × 3 = 39m

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