1.

Draw A DeltaABC in which BC=6 cm, CA=5 cm and AB=4 cm. Construct a triangle similar to it and of scale factor (5)/(3)

Answer»

Solution :Steps of construction
1. Draw a line segment BC=6 cm.
2. Taking B and C as centres, draw TWO arcs of radii 4 cm and 5 cm intersecting each other at A.
3. Join BA and CA. `DeltaABC` is the required triangle.
4. From B, draw any ray BX downwards making at acute angle.
5. Mark five points `B_(1),B_(2),B_(3),B_(4) " and " B_(5)` on BX, such that
`BB_(1)=B_(1)B_(2)=B_(2)B_(3)=B_(3)B_(4)=B_(4)B_(5)`

6. Join `B_(3)C` and from `B_(5)` draw `B_(5)M||B_(3)C` intersecting the extended line segment BC at M.
7. From point M draw MN||CA intersecting the extended line segment BA at N.
Then, `DeltaNBM` is the required triangle whose side is equal to `(5)/(3)` of the CORRESPONDING sides of the `DeltaABC`.
HENCE, `DeltaNBM` is the required triangle.


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