Difference between revisions of "1968 AHSME Problems"
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==Problem 31== | ==Problem 31== | ||
| + | <asy> | ||
| + | draw((0,0)--(10,20*sqrt(3)/2)--(20,0)--cycle,black+linewidth(.75)); | ||
| + | draw((20,0)--(20,12)--(32,12)--(32,0)--cycle,black+linewidth(.75)); | ||
| + | draw((32,0)--(37,10*sqrt(3)/2)--(42,0)--cycle,black+linewidth(.75)); | ||
| + | MP("I",(10,0),N);MP("II",(26,0),N);MP("III",(37,0),N); | ||
| + | MP("A",(0,0),S);MP("B",(20,0),S);MP("C",(32,0),S);MP("D",(42,0),S); | ||
| + | </asy> | ||
| + | |||
| + | In this diagram, not drawn to scale, Figures <math>I</math> and <math>III</math> are equilateral triangular regions with respective areas of <math>32\sqrt{3}</math> and <math>8\sqrt{3}</math> square inches. Figure <math>II</math> is a square region with area <math>32</math> square inches. Let the length of segment <math>AD</math> be decreased by <math>12\tfrac{1}{2}</math> % of itself, while the lengths of <math>AB</math> and <math>CD</math> remain unchanged. The percent decrease in the area of the square is: | ||
| + | |||
| + | <math>\text{(A)}\ 12\tfrac{1}{2}\qquad\text{(B)}\ 25\qquad\text{(C)}\ 50\qquad\text{(D)}\ 75\qquad\text{(E)}\ 87\tfrac{1}{2}</math> | ||
[[1968 AHSME Problems/Problem 31|Solution]] | [[1968 AHSME Problems/Problem 31|Solution]] | ||
| + | |||
==Problem 32== | ==Problem 32== | ||
Revision as of 21:22, 23 September 2014
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
- 31 Problem 31
- 32 Problem 32
- 33 Problem 33
- 34 Problem 34
- 35 Problem 35
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
![[asy] draw((0,0)--(10,20*sqrt(3)/2)--(20,0)--cycle,black+linewidth(.75)); draw((20,0)--(20,12)--(32,12)--(32,0)--cycle,black+linewidth(.75)); draw((32,0)--(37,10*sqrt(3)/2)--(42,0)--cycle,black+linewidth(.75)); MP("I",(10,0),N);MP("II",(26,0),N);MP("III",(37,0),N); MP("A",(0,0),S);MP("B",(20,0),S);MP("C",(32,0),S);MP("D",(42,0),S); [/asy]](http://latex.artofproblemsolving.com/7/2/d/72d20f34a21f4d35e2f011ff1523d4b9e962577c.png)
In this diagram, not drawn to scale, Figures 
and 
are equilateral triangular regions with respective areas of 
and 
square inches. Figure 
is a square region with area 
square inches. Let the length of segment 
be decreased by 
% of itself, while the lengths of 
and 
remain unchanged. The percent decrease in the area of the square is:
Problem 32
Problem 33
Problem 34
Problem 35
Solution
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
