AMC 8 2003 Problem 10
Source:
July 23, 2011
geometrytrapezoidrectangleparallelogram
Problem Statement
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. 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] 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] 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] 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. How many cookies will be in one batch of Trisha's cookies?