+0

# More Geometry 1

0
51
4

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

Guest Oct 3, 2017

#3
+4711
+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
Sort:

#1
+234
+1

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

Mathhemathh  Oct 3, 2017
#2
+76908
+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

CPhill  Oct 4, 2017
#3
+4711
+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
+76908
+1

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

CPhill  Oct 4, 2017

### 19 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details