Question

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

Answer 1

`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.