Question

Which of the following triangles can not be constructed?

• A.
  
  ΔABC in which ∠A = 100°, ∠B = 50° and AB = 5 cm
• B.
  
  ΔABC in which AB = 2 cm, BC = 5 cm and CA = 5 cm
• C.
  
  ΔABC in which ∠A = 30°, ∠B = 60° having perimeter 12 cm
• D.
  
  ΔABC in which AB – AC = 3 cm and ∠B = 45°

Answer 1

The correct option is D


ΔABC in which AB – AC = 3 cm and ∠B = 45°
If two angles of a triangle and the included side is given, then the triangle can be constructed.
Also, if all the three sides of a triangle are given, then the triangle can be easily constructed.
When the perimeter of a triangle is given along with the two base angles, then the triangle can be constructed.
However, if the difference of two sides and an angle is given, then it is not possible to construct the triangle. The measure of third side is required in this case.
Hence, the correct answer is option (d).