Difference between revisions of "2012 AMC 12B Problems/Problem 2"

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== Problem==
 
== Problem==
A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to it's width is 2:1. What is the area of the rectangle
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A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?
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<math>\textbf{(A)}\ 50\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200</math>
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==Solution==
 
==Solution==
 
If the radius is <math>5</math>, then the width is <math>10</math>, hence the length is <math>20</math>. <math>10\times20=200</math>, <math>\boxed{\text{E}}</math>
 
If the radius is <math>5</math>, then the width is <math>10</math>, hence the length is <math>20</math>. <math>10\times20=200</math>, <math>\boxed{\text{E}}</math>

Revision as of 23:34, 24 February 2012

Problem

A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?

$\textbf{(A)}\ 50\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200$


Solution

If the radius is $5$, then the width is $10$, hence the length is $20$. $10\times20=200$, $\boxed{\text{E}}$

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