Multiple choice

Areas of two similar triangles ABC and DEF are 64 sq. cm and 100 sq. cm, respectively. If EF = 1.5 cm, BC is equal to

  1. 1.2 cm

  2. 6 cm

  3. 8 cm

  4. 5 cm
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A Correct answer
Explanation

The ratio of areas of similar triangles is the square of the ratio of their corresponding sides. (Area1 / Area2) = (BC / EF)^2. 64 / 100 = (BC / 1.5)^2. 8 / 10 = BC / 1.5. BC = 0.8 * 1.5 = 1.2 cm.

AI explanation

The ratio of the areas of two similar triangles equals the square of the ratio of their corresponding sides. We set up the proportion 64 divided by 100 equals BC squared divided by 1.5 squared. This simplifies to BC squared equals 0.009 times 1600, resulting in BC equal to 1.2 cm.

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