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#842978 - 10/17/12 01:55 PM Math Fun a-la-Pandora
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 15189
Loc: Ottawa Ontario Canada
This one may look more complicated than Pandora's,
but it turns out "beautifully simple"!
Code:
               A 

            F 


                    

                    E 
    D 


B                      C 

Area of triangle ABC is 13824 square feet.
The length of line segment BD is 4/15 of line segment AB.
The length of line segment CE is 5/12 of line segment AC.
The length of line segment AF is 3/20 of line segment AB.
What is the area of triangle DEF?

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#843131 - 10/18/12 07:20 AM Re: Math Fun a-la-Pandora [Re: CanukDenis]
CCbomber Offline
Addicted Boomer

Registered: 01/16/03
Posts: 3215
Loc: Mojave desert, California
Area of triangle EBC = (5/12) Area of triangle ABC = (5/12)13824 = 5760
Area of triangle ABE = 13824-5760 = 8064

Length of segment DF = Length of sement AB - (4/15 + 3/20)Length of segment AB
= (7/12)Length of segment AB

Area of triangle DEF = (7/12)Area of triangle ABE = (7/12)8064 = 4704

Good one!

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#843146 - 10/18/12 09:08 AM Re: Math Fun a-la-Pandora [Re: CanukDenis]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 15189
Loc: Ottawa Ontario Canada
Yepper CC!

k = Area of triangle ABC (13824)
u = BD/AB (4/15)
v = CE/AC (5/12)
w = AF/AB (3/20)
General case formula:
Area of triangle DEF = k * (1 - u - w) * (1 - v)

13824 * (1 - 4/15 - 3/20) * (1 - 5/12) = 4704

Surprisingly simple formula...
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