Multiple choice

If area of similar triangles ΔABC and ΔDEF be 64 sq. cm and 121 sq. cm and EF = 15.4 cm, then BC equals:

  1. 8 cm

  2. 18 cm

  3. 11.2 cm

  4. 8.2 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For similar triangles, the ratio of areas is the square of the ratio of corresponding sides. Area1/Area2 = (BC/EF)^2. 64/121 = (BC/15.4)^2. Taking square roots, 8/11 = BC/15.4. BC = (8 * 15.4) / 11 = 8 * 1.4 = 11.2 cm.

AI explanation

For similar triangles, the ratio of their areas equals the square of the ratio of their corresponding sides, giving Area(ABC) / Area(DEF) = BC^2 / EF^2. Substituting the given values results in 64 / 121 = BC^2 / 15.4^2. Solving for BC gives BC = 15.4 * (8 / 11) = 11.2 cm. The result is 11.2 cm.

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