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# More Geometry 1

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In the diagram below, we have BE = 7, AB = 5, and [CBDA]=15. What is [CDA]?

Oct 3, 2017

#3
+7348
+2

Also!

Let's call side CD, which is the base of triangle CDA,  " b "  .

Let's call the area of CDA  " a " .

(1/2)(b)(7 + 5)  =  a

(1/2)(b)(12)  =  a

6b  =  a

b  =  a/6

(1/2)(b)(7)  =  a - 15

(7/2)(b)  =  a - 15

(7/2)b + 15  =  a

Plug in  a/6  for  b .

(7/2)(a/6) + 15  =  a

(7/12)a + 15  =  a      Multiply through by  12 .

7a + 180  =  12a

180  =  5a

36  =  a

Oct 4, 2017

#1
+349
+1

Is CPhill's ghost composing an answer right now? Because apparently, CPhill can compose answers while not being online... LOL

Oct 3, 2017
#2
+96106
+1

Parallel to CD, draw line EF through B

We have four triangles EBA, FBA, EBC and FBD....and their combined area is 15

And because triangle EAF  is similar to triangle CAD.....then EB = 5/12 CE  and BF = 5/12 ED ....and the height of EBA and FBA = BA = 5, while the height of EBC and FBD = EB = 7

So we have

Area EBA          +  Area of FBA   +       Area of EBC      +  Area of FBD  =    15

(1/2)(5/12)CE*BA + (1/2)(5/12)ED *BA  + (1/2)(5/12)CE *EB  + (1/2)(5/12)ED *EB  =  15

(1/2)(5/12)CE*5 + (1/2)(5/12)ED *5  + (1/2)(5/12)CE *7  + (1/2)(5/12)ED *7  =  15

[ (1/2)(5/12) CE * (5 + 7) ]  + [ (1/2)(5/12) ED * (5 + 7) ]  = 15

[ (1/2)(5/12) CE * (12) ]  + [ (1/2)(5/12) ED * (12) ]  = 15

[ (1/2)(5/12)* 12  [ CE + ED]  =  15

(60/24) [ CD]  = 15

CD  = 15 * (24/60) =   (1/4) * 24  =  6

So.....area CDA =  (1/2)CD * EA =   (1/2) * 6 * 12  =  36 units^2

Oct 4, 2017
#3
+7348
+2

Also!

Let's call side CD, which is the base of triangle CDA,  " b "  .

Let's call the area of CDA  " a " .

(1/2)(b)(7 + 5)  =  a

(1/2)(b)(12)  =  a

6b  =  a

b  =  a/6

(1/2)(b)(7)  =  a - 15

(7/2)(b)  =  a - 15

(7/2)b + 15  =  a

Plug in  a/6  for  b .

(7/2)(a/6) + 15  =  a

(7/12)a + 15  =  a      Multiply through by  12 .

7a + 180  =  12a

180  =  5a

36  =  a

hectictar Oct 4, 2017
#4
+96106
+1

Hectitar's answer was more concise.....I told my ghost not to be so long-winded!!!!!

Oct 4, 2017