1986 AJHSME Problems/Problem 13: Difference between revisions
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==Solution== | ==Solution== | ||
===Solution 1=== | |||
For the segments parallel to the side with side length 8, let's call those two segments <math>a</math> and <math>b</math>, the longer segment being <math>b</math>, the shorter one being <math>a</math>. | For the segments parallel to the side with side length 8, let's call those two segments <math>a</math> and <math>b</math>, the longer segment being <math>b</math>, the shorter one being <math>a</math>. | ||
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28 is <math>\boxed{\text{C}}</math>. | 28 is <math>\boxed{\text{C}}</math>. | ||
===Solution 2=== | |||
<asy> | |||
unitsize(12); | |||
draw((0,0)--(0,6)--(8,6)--(8,3)--(2.7,3)--(2.7,0)--cycle); | |||
label("$6$",(0,3),W); | |||
label("$8$",(4,6),N); | |||
draw((8,3)--(8,0)--(2.7,0),dashed); | |||
</asy> | |||
Clearly the perimeter of the requested region is the same as the perimeter of the rectangle with the dashed portion. This makes the answer obviously <math>2(6+8)=28\rightarrow \boxed{\text{C}}</math> | |||
==See Also== | ==See Also== | ||
[[ | {{AJHSME box|year=1986|num-b=12|num-a=14}} | ||
[[Category:Introductory Geometry Problems]] | |||
Revision as of 20:07, 22 May 2009
Problem
The perimeter of the polygon shown is
![[asy] draw((0,0)--(0,6)--(8,6)--(8,3)--(2.7,3)--(2.7,0)--cycle); label("$6$",(0,3),W); label("$8$",(4,6),N); [/asy]](http://latex.artofproblemsolving.com/7/a/f/7af65dbc01183104535c1b4a00725861147dddf0.png)
Solution
Solution 1
For the segments parallel to the side with side length 8, let's call those two segments 
and 
, the longer segment being , the shorter one being .
For the segments parallel to the side with side length 6, let's call those two segments 
and 
, the longer segment being , the shorter one being .
So the perimeter of the polygon would be...
Note that 
, and 
.
Now we plug those in:
28 is 
.
Solution 2
![[asy] unitsize(12); draw((0,0)--(0,6)--(8,6)--(8,3)--(2.7,3)--(2.7,0)--cycle); label("$6$",(0,3),W); label("$8$",(4,6),N); draw((8,3)--(8,0)--(2.7,0),dashed); [/asy]](http://latex.artofproblemsolving.com/9/c/2/9c2c60ec3f042b22a74ebe21e5a64a6233dfa214.png)
Clearly the perimeter of the requested region is the same as the perimeter of the rectangle with the dashed portion. This makes the answer obviously 
See Also
| 1986 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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 | ||
