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 | + | 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?
Solution
If the radius is 
, then the width is 
, hence the length is 
. 
, 
