Difference between revisions of "2001 AMC 8 Problems/Problem 8"
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Genevieve puts bracing on her large kite in the form of a cross connecting opposite corners of the kite. How many inches of bracing material does she need? | Genevieve puts bracing on her large kite in the form of a cross connecting opposite corners of the kite. How many inches of bracing material does she need? | ||
| − | <math>\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ | + | <math>\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 37 \qquad \text{(E)}\ 39</math> |
==Solution== | ==Solution== | ||
Revision as of 14:55, 24 October 2016
![[asy] for (int a = 0; a < 7; ++a) { for (int b = 0; b < 8; ++b) { dot((a,b)); } } draw((3,0)--(0,5)--(3,7)--(6,5)--cycle); [/asy]](http://latex.artofproblemsolving.com/f/1/f/f1f9469db4540c2a66686ef837e33ea3746e6e8a.png)
Problem
Genevieve puts bracing on her large kite in the form of a cross connecting opposite corners of the kite. How many inches of bracing material does she need?
Solution
Each diagonal of the large kite is 
times the length of the corresponding diagonal of the short kite since it was made with a grid times as long in each direction. The diagonals of the small kite are 
and 
, so the diagonals of the large kite are 
and 
, and the amount of bracing Genevieve needs is the sum of these lengths, which is 
See Also
| 2001 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
