Q. 215.0( 1 Vote )

# In which of the following cases, a unique triangle can be drawn

A. AB = 4 cm, BC = 8 cm and CA = 2 cm

B. BC = 5.2 cm, ∠B = 90° and ∠C = 110°

C. XY = 5 cm, ∠X = 45° and ∠Y = 60°

D. An isosceles triangle with the length of each equal side 6.2 cm.

Answer :

If we consider BC to be the base of the triangle,

The sum of two sides AB and AC is not greater than the third side. Hence triangle cannot be formed.

In the second option the sum of two angles is 200° which is greater than 180° and hence triangle is not possible as sum of all interior angles of a triangle should be equal to 180°.

In the third option a unique triangle is possible.

For the fourth option, the side length of third side is variable and hence multiple triangle can be formed and hence no unique triangle can be constructed.

So the correct answer is C.

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