Question

Construct a △ ABC in which BC = 6cm, ∠B = 30° and AB – AC = 3.5cm. Justify your construction.

Answer 1

Steps of Construction:

Construct BC = 6 cm

Construct ∠CBX = 30^o

From BX, cut the line segment BD which is equal to AB – AC = 3.5 cm

Join the points CD

Construct a perpendicular bisector of CD which meets BX at the point A

In order to obtain the required triangle ABC join CA

Justification:

We know that A lies on CD which is the perpendicular bisector

So we get

AD = AC

We know that BD = 3.5 cm

It can be written as

AB – AD = 3.5 cm

So we get

AB – AC = 3.5 cm

Therefore, △ ABC is the required triangle.