Example 3 - Chapter 12 Class 9 Herons Formula (Term 1)

Last updated at Sept. 22, 2017 by Teachoo

Transcript

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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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