MathDB

8

Part of 2003 AMC 8

Problems(1)

AMC 8 2003 Problem 8

Source:

7/23/2011
<spanclass=latexbold>BakeSale</span><span class='latex-bold'>Bake Sale</span> Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies di ffer, as shown.
\circ Art's cookies are trapezoids: [asy]size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8)); draw(origin--(5,0)--(5,3)--(2,3)--cycle); draw(rightanglemark((5,3), (5,0), origin)); label("5 in", (2.5,0), S); label("3 in", (5,1.5), E); label("3 in", (3.5,3), N);[/asy]
\circ Roger's cookies are rectangles: [asy]size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8)); draw(origin--(4,0)--(4,2)--(0,2)--cycle); draw(rightanglemark((4,2), (4,0), origin)); draw(rightanglemark((0,2), origin, (4,0))); label("4 in", (2,0), S); label("2 in", (4,1), E);[/asy]
\circ Paul's cookies are parallelograms: [asy]size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8)); draw(origin--(3,0)--(2.5,2)--(-0.5,2)--cycle); draw((2.5,2)--(2.5,0), dashed); draw(rightanglemark((2.5,2),(2.5,0), origin)); label("3 in", (1.5,0), S); label("2 in", (2.5,1), W);[/asy]
\circ Trisha's cookies are triangles: [asy]size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8)); draw(origin--(3,0)--(3,4)--cycle); draw(rightanglemark((3,4),(3,0), origin)); label("3 in", (1.5,0), S); label("4 in", (3,2), E);[/asy]
Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Who gets the fewest cookies from one batch of cookie dough?
<spanclass=latexbold>(A)</span> Art<spanclass=latexbold>(B)</span> Roger<spanclass=latexbold>(C)</span> Paul<spanclass=latexbold>(D)</span> Trisha<spanclass=latexbold>(E)</span> There is a tie for fewest. <span class='latex-bold'>(A)</span>\ \text{Art}\qquad<span class='latex-bold'>(B)</span>\ \text{Roger}\qquad<span class='latex-bold'>(C)</span>\ \text{Paul}\qquad<span class='latex-bold'>(D)</span>\ \text{Trisha}\qquad<span class='latex-bold'>(E)</span>\ \text{There is a tie for fewest.}
geometrytrapezoidrectangleparallelogram