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Question

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please PLEASE IM BEGGING YOU MY TEACHER WILL BE GIVING ME 79 IF I DIDN'T GET THIS .. OR ELSE LOWER THAN THAT. PLEASE
TRIANGLE SIMILARITIES RATIOS AND PROPORTIONS - BARBIE LEE, Wednesday, November 20, 2013 at 8:06am
just delete the parethesis please
TRIANGLE SIMILARITIES RATIOS AND PROPORTIONS - Reiny, Wednesday, November 20, 2013 at 10:52am
The key to this question is to realize that all the right -angled triangles are similar, and have the
ratio of 3:4:5 in the length of their sides.
Mark the two angles in triangle BCD with o and x
( you should be able to see that since XD | BC , so you can mark XDC as o and DCX as x
continue through the other triangles...)

Triangle XDC is similar to triangle DCB
XD:XC:DC = DC:DB:CB = 4:3:5
4p:3p:4
4p/4 = 4/5
4p = 16/5 ----> XD = 16/5
3p/4 = 3/5
3p=12/5 ----> XC = 12/5
and of course ---> CD = 4

now you have all the sides of triangle XDC
Did you notice that
3:4:5 = (5/4)(12/5 : 16/5 : 4) ??

continue in this fashion until you have all sides needed.
TRIANGLE SIMILARITIES RATIOS AND PROPORTIONS - Anonymous, Wednesday, November 20, 2013 at 4:26pm
yes sir ive got that already. i don't know what to do next. please help

Answer 1

For http://imageshack.us/photo/my-images/834/j6wv.jpg/

all the triangles are 3:4:5 So, since
DB=3 and BC=5,
a=4

So, ∆DBC ~ ∆XCD, so
b/3 = 4/5
c/4 = 4/5

b = 3(4/5) = 12/5
c = 4(4/5) = 16/5

∆MDX ~ ∆DBC, but has a hypotenuse of c=16/5. Since it's another 3:4:5 triangle,

d/c = 3/5
g/c = 4/5

d = 3(16/25) = 48/25
g = 4(16/25) = 64/25

Now continue with the other triangles. Just watch the details. They are all 3:4:5 triangles scaled by some amount.