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.
Answers
Answer:
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.
Step-by-step explanation:
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