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Question

ABC is a triangle such that AB=20 cm and AC=5 cm.
Then, which of the following is true about the side BC?
  1. 15 < BC < 25
  2. 10 < BC < 25
  3. 10 < BC < 30
  4. 15 < BC < 30


Solution

The correct option is A 15 < BC < 25
We know that sum of two sides is always greater than the third side.
AB + AC > BC,
since AC = 5 cm and AB = 20 cm
that means BC < 25 cm

Also, the difference between the lengths of any two sides of a triangle is always less than the third side.
AB - AC < BC,
since AC = 5 cm and AB = 20 cm
that means BC > 15 cm

The side BC lies between 15 and 25.

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