Question

The construction of a triangle ABC, given that BC = 3 cm, ∠B = 45° is possible when difference of AB and AC is equal to:

• A. 3.5 cm
• B. 4.5 cm
• C. 3 cm
• D. 2.5 cm

Answer 1

The correct option is D

2.5 cm

BC = 3 cm and $\angle$B = 45${}^{\circ }$

We know that the construction of a triangle is possible if sum of two sides is greater than the third side of the triangle i.e.,

$\Rightarrow$ AB + BC $>$ AC

$\Rightarrow$ BC $>$ AC – AB

$\Rightarrow$ 3 $>$ AC – AB

So, if AC – AB = 2.5 cm, then construction of $\Delta$ABC with given conditions is possible.