Difference between revisions of "2014 AMC 10B Problems/Problem 21"

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==Problem==
 
==Problem==
 
Trapezoid <math> ABCD </math> has parallel sides <math> \overline{AB} </math> of length <math> 33 </math> and <math> \overline {CD} </math> of length <math> 21 </math>. The other two sides are of lengths <math> 10 </math> and <math> 14 </math>. The angles <math> A </math> and <math> B </math> are acute. What is the length of the shorter diagonal of <math> ABCD </math>?
 
Trapezoid <math> ABCD </math> has parallel sides <math> \overline{AB} </math> of length <math> 33 </math> and <math> \overline {CD} </math> of length <math> 21 </math>. The other two sides are of lengths <math> 10 </math> and <math> 14 </math>. The angles <math> A </math> and <math> B </math> are acute. What is the length of the shorter diagonal of <math> ABCD </math>?
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<math> \textbf{(A) }10\sqrt{6}\qquad\textbf{(B) }25\qquad\textbf{(C) }8\sqrt{10}\qquad\textbf{(D) }18\sqrt{2}\qquad\textbf{(E) }26 </math>
  
 
==Solution==
 
==Solution==

Revision as of 12:33, 20 February 2014

Problem

Trapezoid $ABCD$ has parallel sides $\overline{AB}$ of length $33$ and $\overline {CD}$ of length $21$. The other two sides are of lengths $10$ and $14$. The angles $A$ and $B$ are acute. What is the length of the shorter diagonal of $ABCD$?

$\textbf{(A) }10\sqrt{6}\qquad\textbf{(B) }25\qquad\textbf{(C) }8\sqrt{10}\qquad\textbf{(D) }18\sqrt{2}\qquad\textbf{(E) }26$

Solution

See Also

2014 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
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 AMC 10 Problems and Solutions

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