Problem:
A rectangular region is bounded by the graphs of the equations y=a,y=−b, x=−c, and x=d, where a,b,c, and d are all positive numbers. Which of the following represents the area of this region?
Answer Choices:
A. ac+ad+bc+bd
B. ac−ad+bc−bd
C. ac+ad−bc−bd
D. −ac−ad+bc+bd
E. ac−ad−bc+bd
Solution:
Because a,b,c, and d are positive numbers, a>−b and d>−c. Therefore the height of the rectangle is a+b and the width is c+d. The area of the region is (a+b)(c+d)=(A)ac+ad+bc+bd​.
The problems on this page are the property of the MAA's American Mathematics Competitions
