A Δ ABC with sides AB = 16 cm, BC = 12 cm and CA = 18 cm is reduced to Δ A'B'C' such that the smallest side of the image triangle is 4.8 cm. Find the scale factor and use it to find the lengths of the other sides of Δ A'B'C'.
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Question

A Δ ABC with sides AB = 16 cm, BC = 12 cm and CA = 18 cm is reduced to Δ A'B'C' such that the smallest side of the image triangle is 4.8 cm. Find the scale factor and use it to find the lengths of the other sides of Δ A'B'C'.

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KnowledgeBoat · Accepted Answer

Smallest side in Δ ABC (BC) = 12 cm

Smallest side in Δ A'B'C' (B'C') = 4.8 cm

Let scale factor be k.

B'C' = k × BC

k = $\dfrac{B'C'}{BC} = \dfrac{4.8}{12} = \dfrac{2}{5}$

∴ The scale factor is, k = $\dfrac{2}{5}$ .

Now,

⇒ A'B' = k × (AB) = $\dfrac{2}{5} \times 16$ = 6.4 cm

⇒ A'C' = k × (AC) = $\dfrac{2}{5} \times 18$ = 7.2 cm

Hence, scale factor = $\dfrac{2}{5}$ , A'B' = 6.4 cm and A'C' = 7.2 cm.