2010 AMC 10A Problem 2

Question

Four identical squares and one rectangle are placed together to form one large square as shown. The length of the rectangle is how many times as large as its width?

\dfrac{5}{4}

\dfrac{4}{3}

\dfrac{3}{2}

2

3

Answer: B

Concepts:ratio and proportion square (geometry)rectangle

Difficulty rating: 870

Small hint:

Let each small square have side length

s

Big hint:

The rectangle is

4s

long and one small square shorter than the large square

Solution:

WLOG, let the side lengths of the squares be

1.

This means that the length of the rectangle is

4.

We also have that the width must be

4 - 1 = 3.

The desired ratio is then

\dfrac{4}{3}.

Thus, B is the correct answer.