Difference between revisions of "2005 AMC 10B Problems/Problem 23"
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== Solution == | == Solution == | ||
| − | The length of <math>EF</math> is the arithmetic mean of the two parallel bases. Since the base EF is shared between the two smaller trapezoids, you want <math>AB | + | The length of <math>EF</math> is the arithmetic mean of the two parallel bases. Since the base EF is shared between the two smaller trapezoids, you want <math>frac{AB,DC} = \boxed{2}</math>. |
== See Also == | == See Also == | ||
{{AMC10 box|year=2005|ab=B|num-b=22|num-a=24}} | {{AMC10 box|year=2005|ab=B|num-b=22|num-a=24}} | ||
Revision as of 21:58, 23 August 2011
Problem
In trapezoid 
we have 
parallel to 
, 
as the midpoint of 
, and 
as the midpoint of 
. The area of 
is twice the area of 
. What is 
?
Solution
The length of 
is the arithmetic mean of the two parallel bases. Since the base EF is shared between the two smaller trapezoids, you want 
.
See Also
| 2005 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
| 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 | ||
