Multiple choice

Two similar right triangles have corresponding side lengths in a ratio of 3 : 5. If the area of the smaller triangle is 54 square centimeters, what is the area of the larger triangle in square centimeters?

  1. 90

  2. 120

  3. 150

  4. 200
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The ratio of areas of similar triangles is the square of the ratio of their corresponding sides. Area ratio = (3/5)^2 = 9/25. Let A be the area of the larger triangle: 54 / A = 9 / 25. A = (54 * 25) / 9 = 6 * 25 = 150.

AI explanation

For similar triangles, the ratio of their areas is the square of the ratio of their corresponding side lengths. Squaring the given ratio of 3 to 5 gives an area ratio of 9 to 25. Setting up the proportion 9/25 = 54/x and solving for x yields x = 150 square centimeters.

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