Question

Construct a AABC in which AB = 4 cm, B = 60° and altitude CL = 3 cm. Construct a ∆ADE similar to ∆ABC such that each side of ∆ADE is 3/2 times that of the corresponding side of ∆ABC. ​

Answer 1

Steps of construction

1. Draw a line segment AB=4 cm.

2. Construct ∠ABP=60.

3. Draw a line GH∥AB at a distance of 3cm, intersecting BP at C.

4. Join CA. Thus, △ABC is obtained.

5. Extend AB to D such that AD= 3/2 AB =

( 3/2 × 4 )cm = 6cm.

6. Draw DE∥BC, cutting AC produced at E. Then, △ADE is the required triangle similar to △ABC such that each side of △ADE is 3/2 times the corresponding side of △ABC.

Proof: Since DE∥BC, we have : △ADE∼△ABC

∴ AD/AB = DE/BC = AE/AC = 3/2

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