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The adjoining figure, AB || DE. The length of CD is

The adjoining figure, AB || DE. The length of CD is (a) 2.5 cm (b) 2.7 cm (c) 10/3 cm (d) 3.5 cm. Similarity, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

  1. 2.5 cm

  2. 2.7 cm

  3. 103\dfrac{10}{3} cm

  4. 3.5 cm

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Answer

Given AB || DE.

Considering △ABC and △DEC,

∠ ACB = ∠ DCE (Vertically opposite angles are equal)
∠ ABC = ∠ CDE (Alternate angles are equal)

Hence, by AA axiom △ABC ~ △DEC.

Since, both the triangles are similar, hence ratio of their corresponding sides are equal,

∴ABDE=BCCD⇒53=4.5CD⇒CD=3×4.55⇒CD=2.7\therefore \dfrac{AB}{DE} = \dfrac{BC}{CD} \\[1em] \Rightarrow \dfrac{5}{3} = \dfrac{4.5}{CD} \\[1em] \Rightarrow CD = \dfrac{3 \times 4.5}{5} \\[1em] \Rightarrow CD = 2.7

Hence, Option 2 is the correct option.

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