Question

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 ploughing the field at ₹ 18.80 per 10 m²

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Answer 1

$\huge\boxed{\fcolorbox{white}{white}{Question}}$

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 ploughing the field at ₹ 18.80 per 10 m²

$\huge\boxed{\fcolorbox{white}{white}{Answer}}$

⭕Let the sides of the triangle be 25x, 17x and 12x

$\mathtt \red{Given,}$

⭕Perimeter of the triangle = 540 m

⇒ 540 = 25x + 17x + 12x

⇒ 540 = 54x

⇒ x = 540 / 54

⇒ x = 10

$\mathtt \green{Thus, \: sides \: of \: the \: triangle \: are:}$

⇒ 25x = 25 × 10 = 250 m

⇒ 17x = 17 × 10 = 170 m

⇒ 12x = 12 × 10 = 120 m

⭕Let, a = 250 m, b = 170 m and c = 120 m

Therefore, s = a + b + c / 2

⇒ s = 250 + 170 + 120 / 2

⇒ s = 540 / 2

⇒ s = 270

$\mathtt \orange{Therefore,}$

⭕ Area of triangle = √s(s - a)(s - b)(s - c)

= √270 (270 - 250)(270 - 170)(270 - 120)

= √3 × 3 × 3 × 10 × 10 × 2 × 10 × 10 × 10 × 5 × 3

= 3 × 3 × 10 × 10 × 10

= 9000 m²

⭕Cost of ploughing the field at the rate of Rs. 18.80 per 10 m²

= 18.80/10 × 9000

= Rs. 16920