Question

Question 3
Draw a $\Delta$ABC in which BC= 6cm, CA = 5 cm and AB= 4 cm .Construct a triangle similar to it and of scale factor = $\frac{5}{3}$.
Thinking process
Here, scale factor = $\frac{m}{n}=\frac{5}{3}$ i.e m > n then the triangle to be construction is larger than the given through use this concept and then constant the required triangle.

Answer 1

Steps of construction.
1. Draw a line segment BC = 6cm
2. Taking B and C as centres, draw two arcs of radii 4cm and 5cm intersecting each other at A.
3. Join BA and CA $\Delta$ ABC is the required triangle.
4. From B draw any ray BX downward making an acute angle.
5. Mark five points $B_1,B_2,B_3,B_4$ and $B_5$ on BX such that $B{B}_1=B_1{B}_2=B_2{B}_3=B_3{B}_4=B_{4}B{­}_5$

6. Join $B_{3}C$ and from $B_{3}M||B_{3}C$ intersecting the extended segment BC at M.
7. From point M draw MN || CA intersecting line segment BA at N.
Then, $\Delta$NBM is the required triangle whose sides is equal to $\frac{5}{3}$ of the corresponding sides of the $\Delta$ABC.
Hence, $\Delta$ NBM‘s the required triangle.