Ex 12.1, 5
Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. 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 = 540 cm
Semi-Perimeter = s = Perimeter/2
s = 540/2
s = 270 cm
Given Ratio of sides is 12 : 17 : 25
Let sides be a = 12x cm ,b = 17x cm , c = 25x cm
where x is any number
Now,
Perimeter = 540 cm
a + b + c = 540
12x + 17x + 25x = 540
29x + 25x = 540
54x = 540
x = 540/54
x = 10
So,
a = 12x cm
b = 17x cm
c = 25x cm
Area of triangle = ( ( )( )( ))
Putting a =120 cm, b = 170 cm, c = 250 cm & s = 270 cm
Area = (270(270 120)(270 170)(270 250)) cm2
= (270 150 100 20) m2
= ( (27 15 2) (10)5)
= ( (27 30) (10)5)
= ( (27 3) (10)6)
= ( (81) (10)6)
= 81 ((10)6)
= 92 ((10)6)
= (9) (106) ^(1/2)
= (9) (103)
= 9000
Thus, Area = 9000 cm2

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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