Problem:
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
- Art's cookies are trapezoids:
.jpg)
- Roger's cookies are rectangles:
.jpg)
- Paul's cookies are parallelograms:
- Trisha's cookies are triangles:
.jpg)
Each friend uses the same amount of dough, and Art makes exactly cookies.
Who gets the fewest cookies from one batch of cookie dough?
Answer Choices:
A. Art
B. Paul
C. Roger
D. Trisha
E. There is a tie for fewest.
Solution:
Because all of the cookies have the same thickness, only the surface area of their shapes needs to be considered. The surface area of each of Art's trapezoid cookies is . Since he makes cookies, the surface area of the dough is .
Roger's rectangle cookies each have surface area ; therefore, he makes cookies.
Paul's parallelogram cookies each have surface area . He makes cookies.
Trisha's triangle cookies each have surface area . She makes cookies.
So Art makes the fewest cookies.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions