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A right-angled triangle has legs measuring 9 cm and 12 cm. Another right-angled triangle is similar to it and has a hypotenuse of 45 cm. Find the area of the second triangle.

1. 216 cm^2
2. 324 cm^2
3. 405 cm^2
4. 486 cm^2

Correct answer: 486 cm^2

Solution

The first triangle has hypotenuse sqrt(9^2 + 12^2) = 15 cm and area (1/2)(9)(12) = 54 cm^2. The linear scale factor is 45/15 = 3, so areas scale by 3^2 = 9, giving 54 x 9 = 486 cm^2.

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