2001 AMC 10 Problem 15

The two curbs are parallel and the two stripes are parallel, so the crosswalk is a parallelogram. Its sides along the curbs have length $15$ and its other two sides (the stripes) have length $50$.

Compute its area two ways. With the curb segments as bases, the height is the width of the street:
$$\text{Area} = 15 \cdot 40 = 600.$$
With the stripes as bases, the height is exactly the distance $d$ between the stripes:
$$\text{Area} = 50 \cdot d.$$
Equating, $50d = 600$ and $d = 12$.

The answer is $\boxed{\textbf{(C)}\ 12}$.

A parallelogram has two independent base-height pairs, and its area is the same either way. Whenever one height is known and the other is asked for, "area two ways" converts the question into a single multiplication and division. The word "distance between parallel lines" always means the perpendicular distance, which is a height.

Each stripe spans $40$ feet across the street and $50$ feet in length, so it runs $30$ feet along the street (a $30$-$40$-$50$ right triangle). The perpendicular from one stripe to the other, together with the $15$-foot curb segment, forms a right triangle similar to that one, with the $15$ as hypotenuse: $d = 15 \cdot \frac{40}{50} = 12$.

• Treating the 15-foot curb segment as the distance between the stripes (it is measured along the curb, not perpendicular to the stripes).
• Using $30$ (the along-street run of a stripe) as a base together with the wrong height, or mixing up which height belongs to which base.