In a triangle ABC, AC = 40 cm, BC = 4 cm. Find AB.

Given triangle ABC, AC=40 cm, BC= 4 cm.

To find AB=?

We know triangle inequality theorem :-

The sum of any two sides in a triangle is always greater than third side.

1. a+b>c;

2. b+c>a;

3. a+c>b.

Here a=BC=4 cm, b=AC=40 cm, c=AB=?

So we could write following :-

4+40>c;

40+c>4;

4+c>40.

Solving these inequalities, we get

c<44; c>-36; c>36.

side c could not be negative, it would be positive only.

So, 36<c<44

The final answer would be :-

36<AB<44 or AB`in(36,44)`

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