In △ABC, AB=9cm and AC=13cm, then the length of BC could be:
- A4 cm
- B2 cm
- C22 cm
- D20 cm
Solution & Step-by-step Explanation
According to the Triangle Inequality Theorem, the length of any side of a triangle must be:
Less than the sum of the other two sides.
Greater than the absolute difference of the other two sides.
So, for side BC:
AC−AB13−94Let's evaluate the options based on this range:
4cm is not greater than 4.
2cm is not greater than 4.
22cm is not less than 22.
20cm lies perfectly within the range (4,22).
Less than the sum of the other two sides.
Greater than the absolute difference of the other two sides.
So, for side BC:
AC−AB
4cm is not greater than 4.
2cm is not greater than 4.
22cm is not less than 22.
20cm lies perfectly within the range (4,22).