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Question
In a triangle ABC, AB = 4 cm, BC = 4.5 cm and CA = 5 cm. Construct ΔABC. Find the image A'B'C of the ΔABC obtained by enlarging it by a scale factor 2. Measure the sides of the image A'B'C' and show that AB:A'B' = AC:B'C' = CA:C'A'
Solution
Steps of COnstruction of the image: :
1. Draw BC measuring 4cm.
2. With B as the centre and radius 4.5cm, make an arc above BC.
3. With C as the centre and radius 5cm, to cut the previous arc at C.
4. ΔABC us the required triangle.
Scale factor = `"A'B'"/"AB"`
⇒ 2 = `"A'B'"/(4)`
⇒ A'B' = 8cm
Scale factor = `"B'C'"/"BC"`
⇒ 2 = `"B'C'"/(4.5)`
⇒ B'C' = 9cm
Scale factor = `"A'C'"/"AC"`
⇒ 2 = `"A'C'"/(5)`
⇒ A'C' = 10cm
Steps of Construction of the image: :
1. Draw B'C' measuring 9cm.
2. With B' as the centre and radius 8cm, make an arc above B'C'.
3. With C' as the centre and radius 9cm, to cut the pervious arc at C'.
4. ΔA'B'C' is the required image of the ΔABC.
On measuring the sides, we get
`"A'B'"/"AB" = "B'C'"/"BC" = "A'C'"/"AC"` = Scale factor = 2.
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