# Draw a ΔABC in which BC = 6 cm,

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

1. Draw a line segment BC = 6 cm.
2. Taking Sand C as centres, draw two arcs of radii 4 cm and 5 cm intersecting each other at A.
3. Join BA and CA. ΔABC is the required triangle.
4. From B, draw any ray BX downwards making at acute angle.
5. Mark five points B1, B2,B3, B4 and B5 on BX, such that
BB, = B,B2 = B2B3 = B3B4 = B4B5.
6. Join B3C and from B5 draw B5M || B3C intersecting the extended line segment BC at
7. 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.

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