Question

The perimeter of a triangular field is 540 m, and it side are in the ratio 25:17:12.Find the area of the field also find the cost of ploughing the field at rupees 40 per 100m​

Answer 1

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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 field. Also, find the cost of ploughing the field at RS 40 per 100m².

Solution -

Perimeter of triangle =540m

Perimeter of triangle =540mLet the sides of triangle be a, b and c.

On dividing 540 m in the ratio 25:17:12, we get

a=25xcm

b=17xcm

c=12xcm

we know that, perimeter of a triangle = Sum of all sides =a+b+c

540=25x+17x+12x

540=54x

x=10

Sides are:

a=25x=250cm

b=17x=170cm

c=12x=120cm

Let a, b and c be the sides of a triangle.

Let a, b and c be the sides of a triangle.Apply Heron's Formula of find the area of triangle.

Area = √S(S−a)(S−b)(S−c)

Where S = a+b+c / 2

S = 1 / 2 (250+170+120) = 270m

Area = √ (270 (270−250) (270−170) (270−120))

= √(270×20×10×150)

= 9000

Area of triangle is 9000m ²

Now,

The cost of ploughing 100m² =Rs 40

The cost of ploughing 1m² = Rs 40 / 100

Therefore, cost of ploughing 9000m ² =9000× ( 40 / 100 ) = Rs 3600

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I hope this helps you....

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Answer 2

Correct 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 rupees 40 per 100m​ sq.

Given:

• The perimeter of a triangle is 540 m
• The ratio of the sides of the triangle is 25:17:12

To find:

The area of the field

Also the cost of ploughing the field at Rs. 400 per 100m

Now,

Let the sides of the triangle be

• a = 25x m
• b = 17x m
• c = 12x m

So,

The perimeter of a triangle is = sum of all three sides

⇒ 25x + 17x + 12x = 540

⇒ 54x = 540

⇒ x = 540 ÷ 54

[By taking 54 to RHS]

⇒ x = 10

∵ Thus, the value of x = 10

Now,

The side of the triangle is

• a = 25x = 25*10 = 250 m
• b = 17x = 17*10 = 170 m
• c = 12x = 12*10 = 120 m

Finding the area of the field

$= \sqrt{S(S-a)(S-b)(S-c)}\ units\ sq.$

[In which 'S' is 'half of the perimeter', and (a, b, c) are the side of the triangle.]

S = 540 ÷ 2

S = 270

$= \sqrt{270(270-250)(270-170)(270-120)}$

$= \sqrt{270(20)(100)(150)}$

$= \sqrt{\underline{3*3}*3*2*5*(\underline{2*2}*5)*(\underline{2*2}*\underline{5*5})*(2*3*\underline{5*5})}$

$= 3*2*2*5*5\sqrt{\underline{3*3}*\underline{5*5}*\underline{2*2}}$

= 3*2*2*5*5*3*5*2

= 9000 m sq.

Now,

• Ploughing is done in → the area.

The cost of ploughing the field at Rs 40 per 100m

100 m sq. = Rs 40

1m sq. = Rs 0.4

Now,

The cost of ploughing the field at 9000 m sq. is

= 9000 * 0.4 = Rs 3600

Hence,

• The area of the field if 9000 m sq.
• The cost of ploughing the field is Rs. 3600