Question:
Draw a $\triangle A B C$ in which $B C=6 \mathrm{~cm}, C A=5 \mathrm{~cm}$ and $A B=4 \mathrm{~cm}$. Construct a triangle similar to it and of
scale factor $\frac{5}{3}$
Solution:
Steps of construction
- Draw a line segment BC = 6 cm.
- Taking Sand C as centres, draw two arcs of radii 4 cm and 5 cm intersecting each other at A.
- Join BA and CA. ΔABC is the required triangle.
- From B, draw any ray BX downwards making at acute angle.
- Mark five points B1, B2,B3, B4 and B5 on BX, such that
BB, = B,B2 = B2B3 = B3B4 = B4B5. - Join B3C and from B5 draw B5M || B3C intersecting the extended line segment BC at
- From point M draw MN || CA intersecting the extended line segment BA at N.
Then, $\triangle \mathrm{NBM}$ is the required triangle whose sides is equal to $\frac{5}{3}$ of the corresponding sides of the $\triangle A B C$.
Hence, $\triangle N B M$ is the required triangle.