Do you know grade 9 math/a bit about similar triangles? Please help!!!

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1 Answer
Nov 4, 2017

#AC=6#, #BC=10#, #CD=15#, #ED=12#, #EF=16#

Explanation:

The diagram is definitely not drawn to scale!

Let us assume that we are looking for sides of integral length.

Looking at the side of length #20# note that it is the hypotenuse of one scaled copy of the right-angled triangle and one of the legs of another scaled copy of the triangle.

Note that #20# is divisible by #4# and by #5#, so the basic triangle that has been scaled in various ways may be a #3,4,5# triangle.

Note that #9# is divisible by #3# but not by #4#, so we can deduce that:

#ED = 4/3*9 = 12#

#CD = 5/3*9 = 15#

Then

#EF = 4/5*20 = 16#

#AC = 3/4*8 = 6#

#BC = 5/4*8 = 10#

Note that:

#CF = CE+EF=9+16 = 25 = 5/4*20# as required.

enter image source here