2008 AMC 10A Problem 2

Question

A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is

2:1.

The ratio of the rectangle’s length to its width is

2:1.

What percent of the rectangle’s area is inside the square?

12.5

25

50

75

87.5

Let the square have side

s

and express the rectangle’s dimensions in terms of

s

The rectangle is

2s

wide and

4s

long; compare its area to

s^2

Let the side of the square be

s,

so its area is

s^2.

The width of the rectangle is

2s,

and its length is

2 \cdot 2s = 4s,

giving an area of

8s^2.

The fraction inside the square is

\dfrac{s^2}{8s^2} = \dfrac{1}{8} = 12.5\%.

Thus, the correct answer is A.

Problem 2 in other years