Problem:
Six rectangles each with a common base width of 2 have lengths of 1,4,9,16,25, and 36. What is the sum of the areas of the six rectangles?
Answer Choices:
A. 91
B. 93
C. 162
D. 182
E. 202
Solution:
The areas of the six rectangles are 2,8,18,32,50, and 72. Adding yields 182.
OR
The sum of areas is
2â‹…1+2â‹…4+2â‹…9+2â‹…16+2â‹…25+2â‹…36=2(1+4+9+16+25+36)=2â‹…91=182.
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions