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In a rectangle ABCD , point E is on side CD. The area of triangle ADE is one-fourth of the area of quadrilateral ABCE. What is the ratio of the length of segment DE to the length of segment DC? Express your answer as a common fraction.

 Mar 2, 2021
 #1
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If you draw it out, you notce that the area of the rectangle is DC * AD, and that area of ADE = AD*DE/2

So ADE is 1/4 of ABCD

AD*DE/2*4 = DC * AD

AD*DE*2 = DC * AD

DE*2 = DC

So our answer is 1/2 since DE is 1/2 of DC.

 

=^._.^=

 Mar 2, 2021
 #2
avatar+1582 
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In a rectangle ABCD, point E is on the side CD. The area of triangle ADE is one-fourth of the area of quadrilateral ABCE. What is the ratio of the length of segment DE to the length of segment DC? Express your answer as a common fraction.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The ratio of [ADE] to [ABCE] is 1 : 4

 

Let the sides of a rectangle ABCD be 1 and 5        ( [ABCD] = 5)

 

DE = 2   and  DC = 5

 

The ratio of DE to DC is 2/5

 Mar 2, 2021

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