Question

The construction of a triangle ABC, given that BC = 5 cm, ∠B = 45° is not possible when difference of AB and AC is equal to

• A.
  4.9 cm
• B.
  4 cm
• C.
  6 cm
• D.
  3.5 cm

Answer 1

The correct option is C

6 cm
Given: BC = 5 cm, ∠B = 45°
The difference of any two sides in a triangle is always less than the third side.
Let AB > AC.
∴ In ΔABC, AB – AC < BC
⇒ AB – AC < 5 cm
In the case where the difference of AB and AC is 6 cm, is not possible to construct as it is greater than the length of BC.
Hence, the correct answer is option (c).