Two similar triangles have areas of 12 cm2 and 48 sq cm. If the smaller triangle's height is 2.1 cm, what is the larger triangle's corresponding height_________?
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Answer: B. 4.2cm
Explanation
The ratio of areas of two similar triangles equals the square of their height ratio. The area ratio of 12 to 48 simplifies to one-fourth, making the height ratio one-half. Multiplying the smaller triangle height of 2.1 cm by two gives the larger height of 4.2 cm. Similar triangles possess equal corresponding angles and proportional side lengths. The ratio of any corresponding linear dimensions in similar triangles is equal. Area scaling factor in two-dimensional geometry is the square of the linear scale factor.
Geometric similarity principles are widely used in cartography, mapping, and scale modeling. Architects use proportional scaling to convert blueprint dimensions to actual structures. Optics and shadow projection problems frequently involve similar triangle geometry. Choosing 0.525 cm incorrectly divides the smaller height by the scale factor. Choosing 80 percent is a percentage value unrelated to the linear height dimension. Choosing 60 percent is an arbitrary percentage value that violates geometric scaling.
- Subject
- Mathematics
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- Mathematics
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