Diagrams make explanations a lot easier so I created one, see bottom for the picture.
As GHF are all midpoints, that means the lines that connect them are half of the opposite sides.
CD = 2HF
DE = 2GF
CE = 2GH
As HF is 2x CD, and CD = 24:
HF = CD ÷ 2
HF = 24 ÷ 2 = 12
As DE = 2x GF and DF is 9:
DE = 2 x 9
DE = 18
As CE = 2x GH and GH = 7:
CE = 2 x 7
CE = 14
Hope this helps!
There is a slight flaw. She is only correct if all three points are on the same line.
If S is on segment RT, then segment RT can be broken up into RS and ST. Through the segment addition postulate, we can then say
RS+ST = RT
So put another way, Michaela's claim is only true if angle RST is 180 degrees.
However, if angle RST is some other angle, then saying RS+ST = RT is not correct. So Michaela needs to clarify that point S is on segment RT. Or she could say that all three points are on the same straight line.
A diagram is provided below.
Side note: in the figure on the right, RS+ST adds up to something larger than RT. This is due to the triangle inequality theorem. That theorem states that adding any two sides of a triangle adds to something larger than the third remaining side.
