Difference between revisions of "1988 AJHSME Problems/Problem 9"
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draw((0,b)--(11,b)); | draw((0,b)--(11,b)); | ||
} | } | ||
− | draw((0,6)--(2,6)--(1,4)--cycle,linewidth( | + | draw((0,6)--(2,6)--(1,4)--cycle,linewidth(3); |
− | draw((3,4)--(3,6)--(5,4)--cycle,linewidth( | + | draw((3,4)--(3,6)--(5,4)--cycle,linewidth(3)); |
− | draw((0,1)--(3,2)--(6,1)--cycle,linewidth( | + | draw((0,1)--(3,2)--(6,1)--cycle,linewidth(3)); |
− | draw((7,4)--(6,6)--(9,4)--cycle,linewidth( | + | draw((7,4)--(6,6)--(9,4)--cycle,linewidth(3)); |
− | draw((8,1)--(9,3)--(10,0)--cycle,linewidth( | + | draw((8,1)--(9,3)--(10,0)--cycle,linewidth(3)); |
</asy> | </asy> | ||
Revision as of 21:20, 15 December 2020
Problem
An isosceles triangle is a triangle with two sides of equal length. How many of the five triangles on the square grid below are isosceles?
for(int a=0; a<12; ++a) { draw((a,0)--(a,6)); } for(int b=0; b<7; ++b) { draw((0,b)--(11,b)); } draw((0,6)--(2,6)--(1,4)--cycle,linewidth(3); draw((3,4)--(3,6)--(5,4)--cycle,linewidth(3)); draw((0,1)--(3,2)--(6,1)--cycle,linewidth(3)); draw((7,4)--(6,6)--(9,4)--cycle,linewidth(3)); draw((8,1)--(9,3)--(10,0)--cycle,linewidth(3)); (Error compiling LaTeX. 52824a81614fe8726e75b86b84d167d63ca5b343.asy: 13.45: syntax error error: could not load module '52824a81614fe8726e75b86b84d167d63ca5b343.asy')
Solution
The first triangle has two legs of length , the second has two legs of length 2, the leg lengths of the third triangle are , , and , two legs of the fourth triangle have length , and two legs of the fifth triangle have length . Therefore all of the triangles in the diagram except the third are isosceles, and there are are isosceles.
See Also
1988 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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.