Difference between revisions of "2014 AMC 10B Problems/Problem 5"

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==Solution==
 
==Solution==
  
We note that the total length must be the same as the total height because the window a square. Calling the width of each small rectangle <math>2x</math>, and the height <math>5x</math>, we can see that the length is composed of 4 widths and 5 bars of length 2. This is equal to two heights of the small rectangles as well as 3 bars of 2. Thus, <math>4(2x) + 5(2) = 2(5x) + 3(2)</math>. We quickly find that <math>x = 2</math>. The total side length is  <math>4(4) + 5(2) = 2(10) + 3(2) = 26</math>, or <math>\boxed{(A)}</math>.
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We note that the total length must be the same as the total height because the window a square. Calling the width of each small rectangle <math>2x</math>, and the height <math>5x</math>, we can see that the length is composed of 4 widths and 5 bars of length 2. This is equal to two heights of the small rectangles as well as 3 bars of 2. Thus, <math>4(2x) + 5(2) = 2(5x) + 3(2)</math>. We quickly find that <math>x = 2</math>. The total side length is  <math>4(4) + 5(2) = 2(10) + 3(2) = 26</math>, or <math>\boxed{\textbf{(A)}}</math>.
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2014|ab=B|num-b=4|num-a=6}}
 
{{AMC10 box|year=2014|ab=B|num-b=4|num-a=6}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 19:18, 20 February 2014

Problem

Doug constructs a square window using 8 equal-size panes of glass, as shown. The ratio of the height to width of each pane is 5 : 2, and the borders around and between the panes are 2 inches wide. In inches, what is the side length of the square window?

$\textbf {(A) } 26 \qquad \textbf {(B) } 28 \qquad \textbf {(C) } 30 \qquad \textbf {(D) } 32 \qquad \textbf {(E) } 34$

Solution

We note that the total length must be the same as the total height because the window a square. Calling the width of each small rectangle $2x$, and the height $5x$, we can see that the length is composed of 4 widths and 5 bars of length 2. This is equal to two heights of the small rectangles as well as 3 bars of 2. Thus, $4(2x) + 5(2) = 2(5x) + 3(2)$. We quickly find that $x = 2$. The total side length is $4(4) + 5(2) = 2(10) + 3(2) = 26$, or $\boxed{\textbf{(A)}}$.

See Also

2014 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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 AMC 10 Problems and Solutions

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