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

enter image source here

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