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IMO :- D

Area of trapezium ABCD = 1/2 * ( AD+ BC) * AB
28= 1/2 * 14 * AB
AB= 4

Lets Drop Perpendicular from C as H :- Right Angle triangle CHD :-

CH=AB =4
HD= AD-AH =8-6=2

CD^2 =4^2+2^2
CD=2 sqrt (5)
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Bunuel

ABCD has area equal to 28. BC is parallel to AD. BA is perpendicular to AD. If BC is 6 and AD is 8, then what is CD?

A. 2√2
B. 2√3
C. 4
D. 2√5
E. 6

Attachment:
1.jpg

first find the height of the trapezium
1/2 * h* 14 = 28
h=4
now for ∆ ; the base is 2 and h= 4 so side CD ;
2^2+4^2 = CD^2
CD= 2√5
OPTION D
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Bunuel

ABCD has area equal to 28. BC is parallel to AD. BA is perpendicular to AD. If BC is 6 and AD is 8, then what is CD?

A. 2√2
B. 2√3
C. 4
D. 2√5
E. 6


Solution:

The figure is a right trapezoid. We can create the equation to find the height or the length of AB :

28 = (6 + 8)/2 x h

28 = 7h

4 = h

Now draw CE such that E is on AD and CE is perpendicular to AD. We see that CDE is a right triangle with DE = 8 - 6 = 2 and CE = AB = 4. Therefore, we can create an equation to find CD using the Pythagorean theorem,

DE^2 + CE^2 = CD^2

2^2 + 4^2 = CD^2

20 = CD^2

CD = √20 = 2√5

Answer: D
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