2016 AMC 12B Problem 8

Below is the professionally curated solution for Problem 8 of the 2016 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 12B solutions, or check the answer key.

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Concepts:power scaling of length, area, and volume ratio and proportion

Difficulty rating: 1350

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?

$14.0$

$16.0$

$20.0$

$33.3$

$55.6$

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.

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