Question

the perimeter of a triangular field is 240m and its sides are in the ratio of 3:4:5. find the area of the triangle. Also find the cost of ploughing the field at rs.15 per m^2.


Pls answer fast

Answer 1

GIVEN :-

• The perimeter of a triangular field is 240 m.
• Ratio of sides of triangular field are 3:4:5.

TO FIND :-

• The area of the triangular field.
• Cost of ploughing.

SOLUTION :-

Let the ratio constant be "x".

✮ Sides of Triangular Field,

➳ a = 3x.

➳ b = 4x.

➳ c = 5x.

✮ Semi - Perimeter of Triangular Field,

➳ Semi - Perimeter = perimeter/2

➳ Semi - Perimeter = 240/2

➳ Semi - Perimeter = 120 m.

✮ Sides of Triangular Field,

As we know that the semi perimeter of a triangle is given by,

➵ Semi - perimeter (a + b + c)/2

➵ 120 m = (3x + 4x + 5x)/2

➵ 120 = 12x/2

➵ (120 × 2)/12 = x

➵ x = 20.

Now substitute the value of x in the sides of triangle,

➳ a = 3x = 60 m.

➳ b = 4x = 80 m.

➳ c = 5x = 100 m.

✮ Area of triangular field,

As we know that the area of triangle is given by,

✯ Area ∆ = √{s(s - a)(s - b)(s - c)}

➟ Area ∆ = √{120(120 - 60)(120 - 80)(120 - 100)}

➟ Area ∆ = √{120 × 60 × 40 × 20}

➟ Area ∆ = √5760000

➟ Area ∆ = 2400 m².

✮ Cost of pluoghing the field,

➳ Cost = Area × Rate.

➳ cost = 2400 × 15

➳ cost = Rs. 36000.

Answer 2

Answer:

Consider a, b, c as the sides of a triangle in the ratio 25:17:12

It can be written as

a:b:c=25:17:12

So we get

a=25x,b=17x  and c=12x

It is given that

Perimeter = 540 m

So we get

25x+17x+12x=540

On further calculation

54x=540

By division

x=10

By substituting the value of x

a=25x=25(10)=250m

b=17x=17(10)=170m

c=12x=12(10)=120m

We know that  

S=  

2

a+b+c

​  

 

S=  

2

250+170+120

​  

 

By division

S=270m

We know that

Area  

s(s−a)(s−b)(s−c)

​  

 

By substituting the values  

Area=  

270(270−250)(270−170)(270−120)

​  

 

So we get  

Area=  

270×20×100×150

​  

 

It can be written as

Area=  

9×6×5×4×5×100×25×6

​  

 

On further calculation

Area=  

9×36×25×4×100×25

​  

 

So we get

Area=3××6×5×2×10×5

Area=9000m  

2

 

It is given that the cost of ploughing the field is ₹5 per m  

2

 

So the cost of ploughing 9000m  

2

=5×9000

By multiplication

The cost of ploughing 9000m  

2

=₹45000

Therefore, the area of the field is 9000m  

2

 and the cost of ploughing the field is ₹45000.