Multiple choice

If two corresponding sides of two similar triangles are in the ratio $9 : 4$, then what is the ratio of their areas?

  1. $9 : 4$
  2. $3 : 2$
  3. $81 : 16$
  4. $27 : 8$
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C Correct answer
Explanation

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. (9/4)^2 = 81/16.

AI explanation

By the property of similar triangles, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Squaring the given ratio of 9 to 4 gives 81 to 16. The ratio of their areas is 81 : 16.