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Academic Decathlon 2004 State Championship Logic Quiz

Question 01

850 twelve-inch square tiles will be used to tile two square floors of a house.  The sides of the first floor are ten feet longer than the sides of the second floor.  How long are the sides of each floor? 


The first floor is 25 feet square, and the second floor is 15 feet square.

Here's how you solve it.

Let x represent the length of the side of the second floor.

Then the area of the second floor is x² square feet.

The length of the side of the first floor is (x+10) feet.

So the area of the first floor is (x+10)² square feet.

The total area, 850 square feet, can be represented by the following equation:

x² + (x+10)² = 850
x² + x² + 20x + 100 = 850
2x² + 20x - 750 = 0
x² + 10x - 375 = 0
(x+25)(x-15) = 0

So x is either 15 or it is negative twenty five.  Negative answers don't make sense, so x=15.  The answer follows.


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