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In the figure above,ABCD is a rectangle. If the area of triangle AEB

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In the figure above,ABCD is a rectangle. If the area of triangle AEB  [#permalink]

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New post 03 Apr 2017, 08:46
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In the figure above, ABCD is a rectangle. If the area of triangle AEB is 8, what is the area of triangle ACD

A) 8
B) 12
C) 16
D) 24
E) 32

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In the figure above,ABCD is a rectangle. If the area of triangle AEB  [#permalink]

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New post 03 Apr 2017, 10:57
arabella wrote:
In the figure above, ABCD is a rectangle. If the area of triangle AEB is 8, what is the area of triangle ACD

A) 8
B) 12
C) 16
D) 24
E) 32



there are various ways to solve this one

my take
triangle AEB & DEC are congruent
thus both have same area
AB*OE/2 + DC*EM/2 = 8+8
AB=DC ...Given
OE+EM = BC Or AD----(1)
AB(OE+EM)/2=16
FROM (1)
AB*BC= 32=Area of rect.
area of rctangle - 2*area AEB = 32-16=16= Area of triangle AED +BEC
Again Area AED = BEC= 8.
thus area ACD = area AED+ECD
=8+8=16
Ans C
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Re: In the figure above,ABCD is a rectangle. If the area of triangle AEB  [#permalink]

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New post 03 Apr 2017, 23:40
arabella wrote:
In the figure above, ABCD is a rectangle. If the area of triangle AEB is 8, what is the area of triangle ACD

A) 8
B) 12
C) 16
D) 24
E) 32


The approach that I used is:

Angle AEB(x root 2) = 90, EAB(x)=EBA(x)=45. Therefore, it's a 1:1:square root 2 right angled triangle. 1/2*x*x=8 (1/2 base*height =8), x=4.
AC=8, DC=AB=4 root 2, therefore AC^2=AD^2+DC^2
8^2=AD^2+4root 2
AD^2 = 4root 2
Area of triangle ACD = 1/2*4 root 2 * 4 root 2 = 16
Ans C
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Re: In the figure above,ABCD is a rectangle. If the area of triangle AEB  [#permalink]

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New post 03 Apr 2017, 23:51
AEB and CED are congruent. As AB and CD are equal, height of triangle AEB is half of BC.
A(AEB) = 1/2 x AB x height of AEB
= 1/2 x AB x 1/2 BC
= 1/4 AB x BC

Now A(ADC) = 1/2 x DC x AD
= 1/2 x AB x BC
= 2 x A(AEB)
= 2 x 8= 16



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Re: In the figure above,ABCD is a rectangle. If the area of triangle AEB  [#permalink]

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New post 11 Apr 2019, 23:14
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Re: In the figure above,ABCD is a rectangle. If the area of triangle AEB   [#permalink] 11 Apr 2019, 23:14
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