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In the diagram, BD = 5, CE = 4, [ABC] = 24, and [ADE] = 18. Find [ACD].

 Mar 15, 2020
 #1
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The area of a triangle is proportional to its base, so if x is the area of triange ACD, then (x + 20 + 30)/9 = x/7  ==> x = 175.

 Mar 15, 2020
 #2
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If the other triangles are only 24 and 18 how could the area of ACD be 175?

Guest Mar 15, 2020
 #3
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That is a good observation guest.    laugh

 

Let CD be x units in length and let the height be h

so what is BC?

what is DE?

 

You need to find    AreaACD = xh/2

 

Set up formulas for the two areas that you know.

Solve them simultaneously to find the value of xh 

 

Note: you probably can solve for x and h independently but it is easier to find the value of xh

Melody  Mar 16, 2020

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