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Problems(1)

1968 AMC 12 #31 - Three Figures

Source:

1/1/2012
In this diagram, not drawn to scale, figures I\text{I} and III\text{III} are equilateral triangular regions with respective areas of 32332\sqrt{3} and 838\sqrt{3} square inches. Figure II\text{II} is a square region with area 3232 sq. in. Let the length of segment ADAD be decreased by 1212%12\frac{1}{2} \% of itself, while the lengths of ABAB and CDCD remain unchanged. The percent decrease in the area of the square is: [asy] draw((0,0)--(22.6,0)); draw((0,0)--(5.66,9.8)--(11.3,0)--(11.3,5.66)--(16.96,5.66)--(16.96,0)--(19.45,4.9)--(22.6,0)); label("A", (0,0), S); label("B", (11.3,0), S); label("C", (16.96,0), S); label("D", (22.6,0), S); label("I", (5.66, 3.9)); label("II", (14.15,2.83)); label("III", (19.7,2)); [/asy] <spanclass=latexbold>(A)</span> 1212<spanclass=latexbold>(B)</span> 25<spanclass=latexbold>(C)</span> 50<spanclass=latexbold>(D)</span> 75<spanclass=latexbold>(E)</span> 8712<span class='latex-bold'>(A)</span>\ 12\frac{1}{2} \qquad<span class='latex-bold'>(B)</span>\ 25 \qquad<span class='latex-bold'>(C)</span>\ 50 \qquad<span class='latex-bold'>(D)</span>\ 75 \qquad<span class='latex-bold'>(E)</span>\ 87\frac{1}{2}
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