Question

In a triangle ABC if ab =5 cm BC =x cm and ac is = 4 cm, then find the value of the number of such possible triangle for which X is an integer

Answer 1

• 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.

Thank u.

Answer 2

Answer:

The possible triangle would be 7.

Step-by-step explanation:

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.

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