Question

In a triangle abc, if ab = 5 cm, bc = x cm and ac = 4 cm, then find the number of such possible triangles for which x is an integer?

Answer 1

Answer:

Length of third side is greater than difference of remaining two

           = ( 5 - 4 ) = 1 cm.

Length of third side is less than sum of remaining two = ( 5+ 4 ) = 9 cm.

So x =  1 cm < x cm >9 cm.

.........................OR...................................

Since, a triangle ABC is possible if,

AB < BC + CA, AC < AB + BC and BC < AC + AB,

Given,

AB = 5 cm, BC = x, AC = 4 cm,

Thus, if ABC is a triangle,

Then,

x < 5 + 4 = 9

Also, 5 < x + 4 ⇒ 5 - 4 < x ⇒ 1 < x,

Ans, 4 < x + 5 ⇒ - 1 < x,

Thus,

1 < x < 9

∵ Number of integers from 1 to 9 = 7, ( 2, 3, 4, 5, 6, 7, 8)

Hence, there are 7 possible triangles.