Multiple choice

The areas of two similar triangles are 144 sq. cm and 25 sq. cm. If one side of the first triangle is 7.2 cm, the corresponding side of the other triangle is

  1. 3.6 cm

  2. 17.28 cm

  3. 3 cm

  4. 1.25 cm

  5. 41.47 cm
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C Correct answer
Explanation

The ratio of areas of similar triangles is the square of the ratio of their corresponding sides. 144/25 = (7.2/x)^2. Taking the square root, 12/5 = 7.2/x. Thus, 12x = 36, so x = 3.

AI explanation

For similar triangles, the ratio of their areas equals the square of the ratio of their corresponding sides. This gives the proportion 144 divided by 25 equals 7.2 divided by x, where x is the unknown side. Taking the square root of the area ratio yields 12 divided by 5, so 12 divided by 5 equals 7.2 divided by x. Solving this yields x equals 3 cm.

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