Question

Construct an isosceles triangle whose base is 6cm and altitude 4 cm. Then construct another triangle whose sides are `(3)/(4)` times the corresponding sides of the first triangle.

Answer 1

Steps of construction :
1. Draw a line segment BC=6 cm .
2. Draw perpendicular bisector of BC.
3. From mid- point D of BC on perpendicular bisector mark DA=4 cm, join AB and AC.
4. Below BC make an acute angle `angleCBZ`.
5. Along BZ mark off four points `B_(1),(B)_(2),B_(3) and B_(4)` such that `BB_(1)=B_(1)B_(2)=B_(2)B_(3)=B_(3)B_(4)`.
6. Join `B_(4)C`.
7. From `B_(3)` draw `B_(3)E` parallel to `B(4)C` meeting BC at E.
8. From E draw EF||CA meeting BA at F.
Then, `DeltaFBE` is the required triangle.