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Question

In figure, ABCD is a trapezoid in which ¯¯¯¯¯¯¯¯AB is parallel to ¯¯¯¯¯¯¯¯¯CD,¯¯¯¯¯¯¯¯¯AD is perpendicular to ¯¯¯¯¯¯¯¯¯DC, and ¯¯¯¯¯¯¯¯¯AD is perpendicular to ¯¯¯¯¯¯¯¯AB. Calculate the length of ¯¯¯¯¯¯¯¯BC.
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A
3
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B
4
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C
5
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D
6
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E
7
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Solution

The correct option is C 5
In trapezoid ABCD, the ABIICD and AD perpendicular to DC and AD perpendicular to AB
And AB=6,AD=4 and DC=9
Draw perpendicular from B on line DC meet at point E.
Then EC=DCDE=96=3 ( because AB=DE=6)
The in right angle BEC
(BC)2=(BE)2+(EC)2=(4)2+(3)2=16+9=25
BC=25=5

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