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In the given diagram ΔABC ∼ ΔEFG. If ∠ABC = ∠EFG = 60°, then the length of the side FG is:

In the given diagram ΔABC ∼ ΔEFG. If ∠ABC = ∠EFG = 60°, then the length of the side FG is: ICSE 2025 Maths Solved Question Paper.
  1. 15 cm

  2. 20 cm

  3. 25 cm

  4. 30 cm

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Answer

Given, ΔABC ∼ ΔEFG

So, the corresponding sides are in proportion.

ABEF=BCFG1575=3FG15=3FGFG=3×5FG=15 cm\Rightarrow \dfrac{AB}{EF} = \dfrac{BC}{FG}\\[1em] \Rightarrow \dfrac{15}{75} = \dfrac{3}{FG}\\[1em] \Rightarrow \dfrac{1}{5} = \dfrac{3}{FG}\\[1em] \Rightarrow FG = 3 \times 5\\[1em] \Rightarrow FG = 15\text{ cm}

Hence, option 1 is the correct option.

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