Question

ABC is a triangle such that $AB=20cm$ and $AC=5cm$.
Then, which of the following is true about the side BC?

• A. 15 < BC < 25
• B. 10 < BC < 25
• C. 10 < BC < 30
• D. 15 < BC < 30

Answer 1

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

$\therefore$ The side BC lies between 15 and 25.