2010 AMC 10A Problem 2

Below is the professionally curated solution for Problem 2 of the 2010 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 10A solutions, or check the answer key.

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Concepts:ratio and proportion square (geometry)rectangle

Difficulty rating: 870

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?

$\dfrac{5}{4}$

$\dfrac{4}{3}$

$\dfrac{3}{2}$

$2$

$3$

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.

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