Multiple choice

The area of two similar triangles are in ratio 16:81. Find the ratio of its sides.

  1. $\cfrac 19$
  2. $\cfrac 29$
  3. $\cfrac 39$
  4. $\cfrac 49$
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D Correct answer
Explanation

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. If Area1/Area2 = 16/81, then Side1/Side2 = sqrt(16/81) = 4/9.

AI explanation

For similar triangles, the ratio of their corresponding sides is equal to the square root of the ratio of their areas. The area ratio is 16 to 81, so taking the square root of both terms gives the side ratio as 4 to 9. Expressing this ratio as a fraction gives 4/9.

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