Let a, b and c is the sides of the triangle. Then, the perimeter
P = a + b + c
Example 1 :
The sides of a triangle are 12 cm, 6 cm and 8 cm, find the perimeter of the triangle.
Solution :
Let a, b and c are the three sides of the triangle
a = 12 cm, b = 6 cm and c = 8 cm
Perimeter P = 12+6+8
= 26 cm
Therefore the perimeter of a required triangle = 26 cm.
Example 2 :
The sides of a triangle are 5 cm, 7 cm and 9 cm find the perimeter of the triangle.
Solution :
Let a, b and c are the three sides of the triangle
a = 5 cm, b = 7 cm and c = 9 cm
Perimeter P = 5+7+9
= 21 cm
Therefore the perimeter of a required triangle = 21 cm.
Example 3 :
The sides of a triangle are in the ratio 2x, 3x and 5x. If the
perimeter of the triangle is 100 then find the measurement of three
sides.
Solution :
Let a, b and c be the three sides of the triangle
a = 2x, b = 3x and c = 5x
Perimeter P = 2x+3x+5x
= 10 x
Perimeter of triangle = 100 cm
10x = 100
x = 10 cm
Therefore, a = 2x = 2(10) = 20 cm
b = 3x = 3(10) = 30 cm
c = 5x = 5(10) = 50 cm
Example 4 :
The sides of a triangles are in the ratio of 1/2 : 1/3 : 1/4. If the perimeter is 52 cm, then the length of the smallest side is.
Solution :
Ratio of sides of triangle 1/2 : 1/3 : 1/4 to be changed as 6 : 4 : 3
So, side lengths will be 6x, 4x and 3x.
Perimeter = 52
(6x+4x+3x)/12 = 52
13x/12 = 52
x = 52(12/13)
x = 48
So, the smallest side will be 48/2 = 24 cm.
Example 5 :
The area of a triangle is 216 cm2 and its sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is :
Solution :
Let sides be 3x, 4x and 5x.
Area of triangle = √s(s-a)(s-b) (s-c)
s = (3x+4x+5x)/2
s = 12x/2
s = 6x
s-a = 6x-3x = 3x
s-b = 6x-4x = 2x
s-c = 6x-5x = x
√6x(3x)(2x) (x) = 216
3x(2x) = 216
6x2 = 216
x2 = 36
x = 6
So, side lengths are 18 cm, 12 cm and 6 cm.
Perimeter of the triangle = 18 + 12 + 6
= 36 cm
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