KnowledgeBoat Logo
|

Mathematics

Δ ABC with sides AB = 3.6 cm, BC = 4.5 cm and CA = 6 cm is enlarged to Δ A'B'C' such that the largest side of the enlarged triangle is 10 cm. Find the scale factor and use it to find the lengths of the other sides of Δ A'B'C'.

Similarity

2 Likes

Answer

Longest side in Δ ABC (CA) = 6 cm

Longest side in Δ A'B'C' (C'A') = 10 cm

Let scale factor be k.

C'A' = k × CA

k = C′A′CA=106=53\dfrac{C'A'}{CA} = \dfrac{10}{6} = \dfrac{5}{3}.

∴ The scale factor is, k = 53\dfrac{5}{3}

Now,

A'B' = k × (AB) = 53×3.6\dfrac{5}{3} \times 3.6 = 6 cm

B'C' = k × (BC) = 53×4.5\dfrac{5}{3} \times 4.5 = 7.5 cm

Hence, scale factor = 53\dfrac{5}{3}, A'B' = 6 cm and B'C' = 7.5 cm.

Answered By

1 Like

Related Questions