1998 AJHSME Problems/Problem 20


Carpet costs $$21.95$ per square yard and the padding to put under it costs $$2.55$ per square yard. Felix plans to install padding and carpet in the region shown in the diagram. What is the cost of the carpet and padding needed to exactly cover the room?


After both folds are completed, the square would become a triangle that has an area of $\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}$ of the original square.

Since the area is $9$ square inches for $\frac{1}{4}$ of the square, $9\times4=36$ square inches is the area of square $PQRS$

The length of the side of a square that has an area of $36$ square inches is $\sqrt{36}=6$ inches.

Each side is $6$ inches, so the total perimeter is $6\times4=24=\boxed{D}$

See also

1998 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 19
Followed by
Problem 21
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