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2010 AMC 10A Problem 2

Problem 2 of 25EasierAlgebraGeometry

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?

Answer choices

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Solution

WLOG, let the side lengths of the squares be 1.1. This means that the length of the rectangle is 4.4. We also have that the width must be 4−1=3.4 - 1 = 3. The desired ratio is then 43.\dfrac{4}{3}. Thus, B is the correct answer.

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Concepts: ratio and proportion · square (geometry) · rectangle

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.