Problem:
A thin piece of wood of uniform density in the shape of an equilateral triangle with side length inches weighs 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 inches. Which of the following is closest to the weight, in ounces, of the second piece?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The weight of an object of uniform density is proportional to its volume. The volume of the triangular piece of wood of uniform thickness is proportional to the area of the triangle. The side length of the second piece is times the side length of the first piece, so the area of the second piece is times the area of the first piece. Therefore the weight is ounces.
The problems on this page are the property of the MAA's American Mathematics Competitions