¶ 1994 AMC8 Problem 16
Problem:
The perimeter of one square is times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?
Answer Choices:
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Solution:
The perimeter being times larger implies that a side of the larger square is times a side of the smaller square. Thus, since the area of a square is the length of the side squared, it follows that the area of the larger square will be times the area of the smaller square.
The sketch shows that when the perimeter is tripled, it encloses squares equal to the original square:
Since the ratio of areas of similar figures is the square of the ratio of any matching linear part, it follows that the ratio of the areas is .
Use a sample case:
Area of a by square is square unit.
Area of a by square is square units.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions