Example 3
The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area.
Area of triangle = √(s(s−a)(s−b)(s −c))
Here, s is the semi-perimeter,
and a, b, c are the sides of the triangle
Given Perimeter = 300 m
Semi-Perimeter = s =Perimeter/2
s = 300/2
s = 150 m
Given Ratio of sides is 3 : 5 : 7
Let sides be a = 3x meters , b = 5x meters , c = 7x meters
where x is any number
Now,
Perimeter = 300 m
a + b + c = 300
3x + 5x + 7x = 300
15x = 300
x = 300/15
x = 20
So,
a = 3x meter
b = 5x m
c = 7x m
Area of triangle = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐))
Putting a = 60 m , b = 100 m, c = 140 m & s = 150 m
Area = √(150(150−60)(150−100)(150−140)) m2
= √(150×90×50×10) m2
= √( (15×9×5)×(10)4)
= √(15×(3×3)×5×(10)4)
= √(15×(3×5)×3×(10)4)
= √(15×15×3×(10)4)
= √((15)2×3×(10)4)
= √((15)2)×√3× √104
= (15) ×√3× 〖(104)〗^(1/2)
= (15)×√3 × (102)
= (15)×√3 × (100)
= 1500√3
Thus, Area = 1500√3 m2

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.