Question

Using which of the following measurements, can a $△$ ABC be constructed ?

• A. $\angle ={85}^{\circ },\angle B={115}^{\circ },BC=7cm$
• B. $AB=7cm,BC=7cm,\angle C={95}^{\circ }$
• C. $AB=4cm,BC=8cm,CA=5cm$
• D. $AB=5cm,BC=5cm,\angle B={175}^{\circ }$

Answer 1

Answer: (C), (D)

The correct options are
C

$AB=4cm,BC=8cm,CA=5cm$

D

$AB=5cm,BC=5cm,\angle B={175}^{\circ }$

Option A - A triangle cannot be constructed because the sum of $\angle A$ and $\angle B$ exceeds ${180}^{\circ }$.

Option B - A triangle cannot be constructed because it is an isosceles triangle. In an isosceles triangle, angles opposite to equal bases are equal. If AB = BC, then $\angle A=\angle C={95}^{\circ }$ which is not possible as a triangle cnnot have two obtuse angles.

Option C - A triangle can be constructed because the sum of any two sides is greater than the third side.

Option D - A triangle can be constructed because it is an isosceles triangle with one angle as ${140}^{\circ }$. The other two angles will be ${20}^{\circ }$ each.