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A triangle ABC with AB = 3 cm, BC = 6 cm and AC = 4 cm is enlarged to △DEF such that the longest side of △DEF = 9 cm. Find the scale factor and hence, the lengths of the other sides of △DEF.

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Answer

Longest side in △ABC = BC = 6 cm

Corresponding longest side in △DEF = EF = 9 cm.

Scale factor (k) = EFBC=96=32\dfrac{EF}{BC} = \dfrac{9}{6} = \dfrac{3}{2} = 1.5

Triangle ABC is enlarged to DEF. So, the two triangles will be similar.

∴ABDE=BCEF=ACDF=23\therefore \dfrac{AB}{DE} = \dfrac{BC}{EF} = \dfrac{AC}{DF} = \dfrac{2}{3}.

So,

⇒ABDE=23⇒DE=32AB=92=4.5 cm.⇒ACDF=23⇒DF=32AC=122=6 cm.\phantom{\Rightarrow} \dfrac{AB}{DE} = \dfrac{2}{3} \\[1em] \Rightarrow DE = \dfrac{3}{2}AB \\[1em] = \dfrac{9}{2} \\[1em] = 4.5 \text{ cm}. \\[2em] \phantom{\Rightarrow} \dfrac{AC}{DF} = \dfrac{2}{3} \\[1em] \Rightarrow DF = \dfrac{3}{2}AC \\[1em] = \dfrac{12}{2} \\[1em] = 6 \text{ cm}. \\[1em]

Hence, DE = 4.5 cm and DF = 6 cm.

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