9514 1404 393
Answer:
11 73/78 ≈ 11.9359 (not 14)
Explanation:
The similarity statement tells us ...
QS/QR = FG/FH
QS = QR·FG/FH
13x -14 = 154(55/60) = 847/6
Adding 14 = 84/6, we have ...
13x = 931/6
x = 931/78 = 11 73/78 . . . . . . . divide by 13
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Comment on the question
You get a nice integer answer for x if the similarity statement is written ...
∆FGH ~ ∆QRS . . . . . . . note the letters are in alphabetical order
Then you have ...
QS/QR = FH/FG
13x -14 = 154(60/55) = 168
13x = 182
x = 14
This nice answer to a nice similarity statement leads us to believe the question has an error in it.
We suspect you are expected to provide x=14 as the answer, even though that is NOT the answer to the question as written. You may want to discuss this with your teacher.