Difference between revisions of "1958 AHSME Problems/Problem 43"
(Created page with "== Problem == <math> \overline{AB}</math> is the hypotenuse of a right triangle <math> ABC</math>. Median <math> \overline{AD}</math> has length <math> 7</math> and median <math>...") |
Treetor10145 (talk | contribs) (→Solution) |
||
| Line 9: | Line 9: | ||
== Solution == | == Solution == | ||
| − | <math>\fbox{}</math> | + | <asy> |
| + | import geometry; | ||
| + | unitsize(50); | ||
| + | pair A = (0,0), B = (3,0), C = (0, 4); | ||
| + | pair AB = midpoint(A--B), AC = midpoint(A--C); | ||
| + | draw(A--B--C--A); | ||
| + | draw(A--B, StickIntervalMarker(2, 1)); | ||
| + | draw(A--C, StickIntervalMarker(2, 2)); | ||
| + | draw(C--AB); | ||
| + | draw(B--AC); | ||
| + | dot(AB); | ||
| + | dot(AC); | ||
| + | MP("$A$", A, W); | ||
| + | MP("$B$", B, E); | ||
| + | MP("$C$", C, W); | ||
| + | MP("$M$", AB, S); | ||
| + | MP("$N$", AC, W); | ||
| + | label("$x$", A--AB, S); | ||
| + | label("$x$", AB--B, S); | ||
| + | label("$y$", A--AC, SWW); | ||
| + | label("$y$", AC--C, W); | ||
| + | draw(rightanglemark(C, A, B)); | ||
| + | </asy> | ||
| + | <math>\fbox{D}</math> | ||
== See Also == | == See Also == | ||
Revision as of 11:30, 23 February 2018
Problem
is the hypotenuse of a right triangle 
. Median 
has length 
and median 
has length 
. The length of is:
Solution
import geometry;
unitsize(50);
pair A = (0,0), B = (3,0), C = (0, 4);
pair AB = midpoint(A--B), AC = midpoint(A--C);
draw(A--B--C--A);
draw(A--B, StickIntervalMarker(2, 1));
draw(A--C, StickIntervalMarker(2, 2));
draw(C--AB);
draw(B--AC);
dot(AB);
dot(AC);
MP("$A$", A, W);
MP("$B$", B, E);
MP("$C$", C, W);
MP("$M$", AB, S);
MP("$N$", AC, W);
label("$x$", A--AB, S);
label("$x$", AB--B, S);
label("$y$", A--AC, SWW);
label("$y$", AC--C, W);
draw(rightanglemark(C, A, B));
(Error making remote request. Unknown error_msg)
See Also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 42 |
Followed by Problem 44 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
