Question

Draw a ∆ABC in which BC = 5.4 cm, ∠B = 45° and ∠A = 105°. Now, construct a triangle similar to ∆ABC each of whose sides is 4/3 of the corresponding side of ∆ABC.

Answer 1

Given BC = 5.4 cm, ∠B = 45°, ∠A = 105°
Step of construction
1.Draw BC = 5.4 cm
2.Construct ∠XBC = 45° and
∠YCB = 180° – (45° + 105°) = 30° at B and C, respectively intersecting at A.

3. Below BC, make an acute ∠CBZ
4. Along BZ, mark off 4 arcs: B₁, B₂, B₃, B₄ such that
BB₁ = B₁B₂ = B₂B₃ = B₃B₄
5. Join B₃ C
6. From B₄, draw B₄ D || B₃ C, meeting BC produced at D
7. From D, draw DE || AC, meeting BA produced at E.

Then EBD is the required triangle whose sides are 4/3times the corresponding sides of ∆ABC