Difference between revisions of "2018 AMC 10A Problems/Problem 13"
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A paper triangle with sides of lengths 3,4, and 5 inches, as shon, is folded so that point <math>A</math> falls on point <math>B</math>. What is the length in inches of the crease? | A paper triangle with sides of lengths 3,4, and 5 inches, as shon, is folded so that point <math>A</math> falls on point <math>B</math>. What is the length in inches of the crease? | ||
| − | + | <asy> | |
draw((0,0)--(4,0)--(4,3)--(0,0)); | draw((0,0)--(4,0)--(4,3)--(0,0)); | ||
| − | label(" | + | label("$A$", (0,0), SW); |
| − | label(" | + | label("$B$", (4,3), NE); |
| − | label(" | + | label("$C$", (4,0), SE); |
| − | label(" | + | label("$4$", (2,0), S); |
| − | label(" | + | label("$3$", (4,1.5), E); |
| − | label(" | + | label("$5$", (2,1.5), NW); |
fill(origin--(0,0)--(4,3)--(4,0)--cycle, gray); | fill(origin--(0,0)--(4,3)--(4,0)--cycle, gray); | ||
| − | + | </asy> | |
<math>\textbf{(A) } 1+\frac12 \sqrt2 \qquad \textbf{(B) } \sqrt3 \qquad \textbf{(C) } \frac74 \qquad \textbf{(D) } \frac{15}{8} \qquad \textbf{(E) } 2 </math> | <math>\textbf{(A) } 1+\frac12 \sqrt2 \qquad \textbf{(B) } \sqrt3 \qquad \textbf{(C) } \frac74 \qquad \textbf{(D) } \frac{15}{8} \qquad \textbf{(E) } 2 </math> | ||
Revision as of 13:03, 8 February 2018
A paper triangle with sides of lengths 3,4, and 5 inches, as shon, is folded so that point 
falls on point 
. What is the length in inches of the crease?
![[asy] draw((0,0)--(4,0)--(4,3)--(0,0)); label("$A$", (0,0), SW); label("$B$", (4,3), NE); label("$C$", (4,0), SE); label("$4$", (2,0), S); label("$3$", (4,1.5), E); label("$5$", (2,1.5), NW); fill(origin--(0,0)--(4,3)--(4,0)--cycle, gray); [/asy]](http://latex.artofproblemsolving.com/2/1/1/21145c9f39a3f3cd34317f8b1f8e3f3541c3c477.png)
