2007 CEMC Pascal Problems/Problem 3

Problem

What fraction of the area of rectangle $ABCD$ is the area of the shaded square?

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$\text{ (A) }\ \frac{1}{15} \qquad\text{ (B) }\ \frac{1}{8} \qquad\text{ (C) }\ \frac{1}{10} \qquad\text{ (D) }\ \frac{1}{4} \qquad\text{ (E) }\ \frac{1}{12}$

Solution 1

We can simply divide the area of the shaded region by the total area of the rectangle.

Since the square has a side length of $1$ , its area is $1^{2} = 1$ .

Since the area has a height of $3$ and a width of $5$ , its area is $3 \times 5 = 15$ .

Finding the fraction, we get $\boxed {\textbf {(A) } \frac{1}{15}}$ .

~anabel.disher

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2007 CEMC Pascal Problems/Problem 3

Problem

Solution 1