Question

If two sides of a triangle are 8 cm and 13 cm, then the length of the third side is between a cm and b cm. Find the values of a and b such that a is less than b.

Answer 1

sum of 2 side should be greater than 3rd side

and diffrence of 2 sides should be smaller than 3rd thus

let side z then 13+8>z>13-8

21.>z>5

side should between 21 and 5 thus b=21 and a=5

Answer 2

Answer:

Let the length third number be x

Third side is between a and b

ie b >x> a -------------'( 1 )

But two sides of a triangle are 8cm. And 13 cm.

Sum of any two sides is greater then third

Therefore 8+13 > x

= 21 > x ............(2)

Difference of any 2 sides is less than the 3rd side

Therefore 13 - 8 < x

5<x .........(3)

From equation 2 and 3

21> x >5..........(4)

From equation no 1 and 4

a =21 b =5