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 field. Also, find the cost of ploughing the field at Rs 5 per m²

Answer 1

Answer :

• Area of triangle is 9000 m²
• 45000 is the cost of plouhging the field at Rs.5 per m²

Given :

• The perimeter of a triangular field is 540m
• Sides are in the ratio 25:17:12

To find :

• Area of the filed
• Cost of plouhging the field at Rs . 5 per m²

Solution :

Given,

Sides are in the ratio 25 : 17 : 12 so,

• Let the sides be 25x , 17x and 12x

• Perimeter is 540 so,

➝ 25x + 17x + 12x = 540

➝ 54x = 540

➝ x = 540/54

➝ x = 10

• 25x = 25(10) = 250
• 17x = 17(10) = 170
• 12x = 12(10) = 120

So, Sides are 250 , 170 , 120.

We know that,

• Semi perimeter = a + b + c / 2

Where

• a is 250
• b is 170
• c is 120

➝ s = a + b + c / 2

➝ s = 250 + 170 + 120 / 2

➝ s = 540/2

➝ s = 270

Semi perimeter of triangle is 270

Finding the Area of triangle

We know that heron's formula :

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

Where,

• s is semi perimeter of triangle
• a , b , c is sides

➝ √s(s - a) (s - b) (s - c)

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

➝ √270 × 20 × 10 × 150

➝ √81000000

➝ 9000 m²

Hence, Area of triangle is 9000 m²

Finding the cost of plouhging the field at Rs.5 per m² :

➝ 9000 × 5

➝ Rs.45000

Hence , 45000 is the cost of plouhging the field at Rs.5 per m²