ACT Math · Triangles and similarity

A figure with a perimeter of 24 is enlarged by a scale factor of 2.5. What is the perimeter of the enlarged figure?

A figure with a perimeter of 24 is enlarged by a scale factor of 2.5. What is the perimeter of the enlarged figure?

Answer and explanation

Answer: H: 60

When a figure is enlarged by a scale factor kk, every length, including the perimeter, is multiplied by kk. So the new perimeter is 24⋅2.5=6024\cdot2.5=60, choice H. Areas would scale by k2k^2, but perimeter is a length. Choice G (4848) uses a scale factor of 22 instead of 2.52.5. Choice F (26.526.5) adds 2.52.5 instead of multiplying. Choice J (150150) multiplies by 2.52=6.252.5^2=6.25, which is the factor for area. Check that the enlarged perimeter is larger than the original, by a factor of 2.52.5.

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