Question

ABC is a triangle such that $AB=15cm$ and $AC=5cm$. The side BC lies between and .

• A. 10
• B. 20
• C. 8
• D. 12

Answer 1

Answer: (A), (B)

The correct options are
A 10
B 20

We know that sum of two sides is always greater than the third side.
AB + AC > BC,
since $AC$ = 5 cm and $AB$ = 15 cm
that means $BC$ < 15 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 $AB$ = 15 cm
that means $BC$ > 10 cm

$\therefore$ The side BC lies between 10 and 20.