MathDB
Circle Inscribed in Rectangle

Source: 2012 AMC10B Problem #2

February 23, 2012
geometryrectangleratioAMC

Problem Statement

A circle of radius 55 is inscribed in a rectangle as shown. The ratio of the the length of the rectangle to its width is 2 : 12\ :\ 1. What is the area of the rectangle?
[asy] draw((0,0)--(0,10)--(20,10)--(20,0)--cycle); draw(circle((10,5),5)); [/asy]
<spanclass=latexbold>(A)</span> 50<spanclass=latexbold>(B)</span> 100<spanclass=latexbold>(C)</span> 125<spanclass=latexbold>(D)</span> 150<spanclass=latexbold>(E)</span> 200 <span class='latex-bold'>(A)</span>\ 50\qquad<span class='latex-bold'>(B)</span>\ 100\qquad<span class='latex-bold'>(C)</span>\ 125\qquad<span class='latex-bold'>(D)</span>\ 150\qquad<span class='latex-bold'>(E)</span>\ 200