2014 AMC 8 Problems/Problem 6
Contents
[hide]Problem
Six rectangles each with a common base width of have lengths of , and . What is the sum of the areas of the six rectangles?
Solution
The sum of the areas is equal to . This is equal to , which is equal to . This is equal to our final answer of .
Solution 2
we can just multiply the common width 2 by each of the lengths 1 by 1, the sum would be 182. This is slow and grouping the lengths is easier to. The answer is still .
Solution 3
The formula for a consecutive perfect squared sum is , where is the number of terms from 1.
Multiplying by the constant length 2 for area gives .
Plugging in gives .
~PeterDoesPhysics
Video Solution (CREATIVE THINKING)
~Education, the Study of Everything
Video Solution
https://youtu.be/SvjJETtxQnk ~savannahsolver
See Also
2014 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AJHSME/AMC 8 Problems and Solutions |
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