Difference between revisions of "2014 AMC 8 Problems/Problem 14"
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| − | + | Rectangle <math>ABCD</math> and right triangle <math>DCE</math> have the same area. They are joined to form a trapezoid, as shown. What is <math>DE</math>? | |
| + | <asy> | ||
| + | size(250); | ||
| + | defaultpen(linewidth(0.8)); | ||
| + | pair A=(0,5),B=origin,C=(6,0),D=(6,5),E=(18,0); | ||
| + | draw(A--B--E--D--cycle^^C--D); | ||
| + | draw(rightanglemark(D,C,E,30)); | ||
| + | label("$A$",A,NW); | ||
| + | label("$B$",B,SW); | ||
| + | label("$C$",C,S); | ||
| + | label("$D$",D,N); | ||
| + | label("$E$",E,S); | ||
| + | label("$5$",A/2,W); | ||
| + | label("$6$",(A+D)/2,N); | ||
| + | </asy> | ||
| + | |||
| + | <math> \textbf{(A) }12\qquad\textbf{(B) }13\qquad\textbf{(C) }14\qquad\textbf{(D) }15\qquad\textbf{(E) }16 </math> | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2014|num-b=13|num-a=15}} | {{AMC8 box|year=2014|num-b=13|num-a=15}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 18:41, 26 November 2014
Rectangle 
and right triangle 
have the same area. They are joined to form a trapezoid, as shown. What is 
?
![[asy] size(250); defaultpen(linewidth(0.8)); pair A=(0,5),B=origin,C=(6,0),D=(6,5),E=(18,0); draw(A--B--E--D--cycle^^C--D); draw(rightanglemark(D,C,E,30)); label("$A$",A,NW); label("$B$",B,SW); label("$C$",C,S); label("$D$",D,N); label("$E$",E,S); label("$5$",A/2,W); label("$6$",(A+D)/2,N); [/asy]](http://latex.artofproblemsolving.com/c/3/5/c358884777664e69762bbb69b74c260349626ff4.png)
See Also
| 2014 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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. 
