1989 AJHSME Problems/Problem 24
Problem
Suppose a square piece of paper is folded in half vertically. The folded paper is then cut in half along the dashed line. Three rectangles are formed-a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?
![[asy] draw((0,0)--(0,8)--(6,8)--(6,0)--cycle); draw((0,8)--(5,9)--(5,8)); draw((3,-1.5)--(3,10.3),dashed); draw((0,5.5)..(-.75,4.75)..(0,4)); draw((0,4)--(1.5,4),EndArrow); [/asy]](http://latex.artofproblemsolving.com/6/a/b/6ab13c6ad222a415ca8ff4bfb6135d981e1c657c.png)
Solution
From here on, a blue line represents a cut, the dashed line represents the fold.
![[asy] draw((0,0)--(4,0)--(4,4)--(0,4)--cycle,linewidth(1)); draw((1,0)--(1,4),blue+linewidth(1)); draw((2,0)--(2,4),dashed); draw((3,0)--(3,4),blue+linewidth(1)); label("$x$",(0.5,4),N); label("$x$",(1.5,4),N); label("$x$",(2.5,4),N); label("$x$",(3.5,4),N); label("$4x$",(0,2),W); [/asy]](http://latex.artofproblemsolving.com/8/7/e/87eaf90020921c5f0b0a692a128d18a6aad5a735.png)
From the diagram, we can tell the perimeter of one of the small rectangles is 
and the perimeter of the large rectangle is 
. The desired ratio is ![\[\frac{10x}{12x}=5/6\rightarrow \boxed{\text{E}}\]](http://latex.artofproblemsolving.com/1/1/6/1166e492f670529bdb1c5b452f3f9ec2e43d95e5.png)
See Also
| 1989 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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 | ||
