Let the common ratio between the sides of the given triangle be x.
Therefore, the side of the triangle will be 12x, 17x, and 25x.
Perimeter of this triangle = 540 cm
12x + 17x + 25x = 540 cm
54x = 540 cm
x = 10 cm
Sides of the triangle will be 120 cm, 170 cm, and 250 cm.
`s="perimeter of triangle"/2=540/2=270cm`
By Heron's formula,
`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`
`=[sqrt(270(270-120)(270-170)(270-250))]cm^2`
`=[sqrt(270xx150xx100xx20)]cm^2`
= 9000 cm2
Therefore, the area of this triangle is 9000 cm2.
Last updated at Sept. 22, 2017 by
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
Solution:
Given: Ratio of sides of the triangle and its perimeter.
By using Heron’s formula, we can calculate the area of a triangle.
Heron's formula for the area of a triangle is: Area = √s(s - a)(s - b)(s - c)
Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the perimeter of the triangle
Since the ratios of the sides of the triangle are given as 12:17:25
So, we can assume the length of the sides of the triangle as 12x cm, 17x cm, and 25x cm.
So the perimeter of the triangle will be
Perimeter = 12x + 17x + 25x
12x + 17x + 25x = 540 (given)
54x = 540
x = 540/54
x = 10 cm
Therefore, the sides of the triangle:
12x = 12 × 10 = 120 cm, 17x = 17 × 10 = 170 cm, 25x = 25 × 10 = 250 cm
a = 120cm, b = 170 cm, c = 250 cm
Semi-perimeter(s) = 540/2 = 270 cm
By using Heron’s formula,
Area of a triangle = √s(s - a)(s - b)(s - c)
= √270(270 - 120)(270 - 170)(270 - 250)
= √270 × 150 × 100 × 20
= √81000000
= 9000 cm2
Area of the triangle = 9000 cm2.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 12
Video Solution:
Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.
Class 9 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 5
Summary:
It is given that sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. We have found that its area is 9000 cm2.
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