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Mathematics

In the adjoining figure, DE ∥ BC. If AD : DB = 3 : 1 and EA = 3.3 cm, then AC equals:

  1. 1.1 cm

  2. 4 cm

  3. 4.4 cm

  4. 5.5 cm

On a map drawn to a scale of 1 : 25000, a triangular plot LMN of land has the following measurements : Similarity of Triangles, RSA Mathematics Solutions ICSE Class 10.

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Answer

Since, DE // BC,

By basic proportionality theorem,

⇒ADDB=AEEC⇒31=3.3EC⇒EC=3.33⇒EC=1.1 cm.\Rightarrow \dfrac{AD}{DB} = \dfrac{AE}{EC} \\[1em] \Rightarrow \dfrac{3}{1} = \dfrac{3.3}{EC} \\[1em] \Rightarrow EC = \dfrac{3.3}{3} \\[1em] \Rightarrow EC = 1.1 \text{ cm.}

From figure,

AC = AE + EC

AC = 3.3 + 1.1 = 4.4 cm.

Hence, option 3 is the correct option.

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