Math Help −> Puzzles −> AD 2004 state championship logic quiz −> Question 14 −> Answer

Academic Decathlon 2004 State Championship Logic Quiz

Question 14

You are given two squares. The larger square, Square "A", has sides that are three times as long as the smaller Square "B". The total area of the two squares is 490 square feet. What are the areas of the two squares?

Answer:

Square A's area is 441 square feet,
Square B's area is 49 square feet.

Since the sides of Square A are three times as long as the sides of Square B, it follows that the area of Square A is nine times as big as the area of Square B. (Try a few examples yourself, and you'll see this is always true.) So Square A's area is 9/10 of the total area. Square B's area is 1/10 of the total area. The result follows.

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