## FINDING THE PERIMETER OF A TRIANGLE

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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