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Question

Question 5
Draw a ΔABC in which AB = 5 cm , BC = 6 cm and ABC=60. Construct a triangle similar to ABC with scale factor 57. Justify the construction.

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Solution

Steps of construction

1. Draw a line segment AB= 5 cm
2. From Point B, draw ABY=60 on which take BC = 6cm
3. Join AC, ΔABC is the required triangle.
4. From A, draw any ray AX downwards marking an acute angle.
5. Mark 7 points B1,B2,B3,B4,B5,B6 and B7 on AX. Such that AB1=B1B2=B2B3=B3B4=B4B5=B5B6=B6B7
6. Join B7B and from B5 draw B5MB7B intersecting AB at M
7. From point M draw MNBC intersecting AC at N. then ΔAMN is the required triangle whose sides are equal to 57 of the corresponding sides of the ΔABC
Justification
Here B5MB7B (by construction)

AMBM=52

Now, ABAM=AM+MBAM

=1+MBAM=1+25=75

Also, MNBC

ΔAMNΔABC

Therefore AMAB=ANAC=NMBC=57

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