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Mathematics

In ΔABC, DE ∥ BC such that ADDB=35\dfrac{AD}{DB} = \dfrac{3}{5}. If AC = 5.6 cm, then AE = ?

  1. 2.1 cm

  2. 2.8 cm

  3. 3.1 cm

  4. 4.2 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

By basic proportionality theorem,

If a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides those two sides in the same ratio.

Since DE ∥ BC in ΔABC,

⇒ADDB=AEEC⇒35=AEAC−AE⇒35=AE5.6−AE⇒3×(5.6−AE)=5AE⇒16.8−3AE=5AE⇒5AE+3AE=16.8⇒8AE=16.8⇒AE=16.88⇒AE=2.1 cm.\Rightarrow \dfrac{AD}{DB} = \dfrac{AE}{EC} \\[1em] \Rightarrow \dfrac{3}{5} = \dfrac{AE}{AC - AE} \\[1em] \Rightarrow \dfrac{3}{5} = \dfrac{AE}{5.6 - AE} \\[1em] \Rightarrow 3 \times (5.6 - AE) = 5AE \\[1em] \Rightarrow 16.8 - 3AE = 5AE \\[1em] \Rightarrow 5AE + 3AE = 16.8 \\[1em] \Rightarrow 8AE = 16.8 \\[1em] \Rightarrow AE = \dfrac{16.8}{8} \\[1em] \Rightarrow AE = 2.1 \text{ cm.}

Hence, option 1 is the correct option.

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