The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle. Also, find the cost of cultivating the field at ₹ 24.60 per 100 m².
Mensuration
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The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle. Also, find the cost of cultivating the field at ₹ 24.60 per 100 m2.

KnowledgeBoat · Accepted Answer

It is given that the sides of a triangular field are in the ratio 25 : 17 : 12. Let the lengths of the sides be 25x, 17x and 12x. Given, The perimeter of a triangular field is 540 m. Perimeter = sum of all sides of triangle ⇒ 540 = 25x + 17x + 12x ⇒ 540 = 54x ⇒ x = ⇒ x = 10. So the sides of the triangle are ⇒ 25x = 25 × 10 = 250 m ⇒ 17x = 17 × 10 = 170 m ⇒ 12x = 12 × 10 = 120 m Let a = 250 m, b = 170 m, c = 120 m. s = = 270 m. (s - a) = (270 - 250) m = 20 m. (s - b) = (270 - 170) m = 100 m. (s - c) = (270 - 120) m = 150 m. We know that, Rate = ₹ 24.60 per 100 m2 = ₹ per m2. Cost = Area of triangle × Rate = 9000 × = 24.60 × 90 = ₹ 2,214. Hence, area of field = 9000 m2 & cost of cultivating the field = ₹ 2,214.

Mathematics

The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle. Also, find the cost of cultivating the field at ₹ 24.60 per 100 m².

Mensuration

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