Difference between revisions of "2014 AMC 8 Problems/Problem 6"

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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?
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==Problem==
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Six rectangles each with a common base width of <math>2</math> have lengths of <math>1, 4, 9, 16, 25</math>, and <math>36</math>. What is the sum of the areas of the six rectangles?
  
 
<math>\textbf{(A) }91\qquad\textbf{(B) }93\qquad\textbf{(C) }162\qquad\textbf{(D) }182\qquad \textbf{(E) }202</math>
 
<math>\textbf{(A) }91\qquad\textbf{(B) }93\qquad\textbf{(C) }162\qquad\textbf{(D) }182\qquad \textbf{(E) }202</math>
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==Solution==
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The sum of the areas is equal to <math>2\cdot1+2\cdot4+2\cdot9+2\cdot16+2\cdot25+2\cdot36</math>. This is equal to <math>2(1+4+9+16+25+36)</math>, which is equal to <math>2\cdot91</math>. This is equal to our final answer of <math>\boxed{\textbf{(D)}~182}</math>.
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2014|num-b=5|num-a=7}}
 
{{AMC8 box|year=2014|num-b=5|num-a=7}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 21:13, 24 January 2021

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?

$\textbf{(A) }91\qquad\textbf{(B) }93\qquad\textbf{(C) }162\qquad\textbf{(D) }182\qquad \textbf{(E) }202$

Solution

The sum of the areas is equal to $2\cdot1+2\cdot4+2\cdot9+2\cdot16+2\cdot25+2\cdot36$. This is equal to $2(1+4+9+16+25+36)$, which is equal to $2\cdot91$. This is equal to our final answer of $\boxed{\textbf{(D)}~182}$.

See Also

2014 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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