2016 AMC 12B Problem 8

Problem 8 of 25EasierGeometry Arithmetic

A thin piece of wood of uniform density in the shape of an equilateral triangle with side length

3

inches weighs

12

ounces. A second piece of the same type of wood, with the same thickness, also in the shape of an equilateral triangle, has side length

5

inches. Which of the following is closest to the weight, in ounces, of the second piece?

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Solution

Weight is proportional to area, and area scales with the square of the side length. The second side is

\tfrac53

times the first, so its weight is

12\cdot\left(\dfrac53\right)^2=\dfrac{100}{3}\approx33.3

ounces. Thus, the correct answer is D.

Tagged: power scaling of length, area, and volume · ratio and proportion