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Do you need a letter
sorry i forgot to put the answer choices
A. 7 B. 10 C. 14 D. 20
Looks like the T is in the center, which makes QT = TS and PT = TR, so 2 equations would be needed
how would i go about setting up the equations
Like for the QT = TS, you said QT was 2x and TS was y+3, so that equation is y+3 = 2x What would the other one be?
x+2=y , right?
Right, so now you have to find an X and Y value by using the tedious substitution method to find those values to satisfy both equations It'll take a while, so ill work it with you
Oh, but first Since we had y+3 = 2x for the first one, we have to get y by itself.
could y=5 ?
I don't know I'm not very smart
You did get the numeral right, but not the variable Oh, don't be like that. This problem takes alot of time
so x=5 ?
Right! Plugging that into both those equations will get you the same y value, which is...?
it is 7
Correct! Now we can finally find the answer to this So we said originally QT = TS and PT = TR, which means QT + TS is one length and PT + TR is another So we add original lengths (2x) + (y+3) = (y) + (x+2) = We know y =7 and x=5 After finding those two answer, the larger number is the longer side
so is it 7 or 14
so the longer side is 20 because (2x5)+(7+3)=20 and that is greater than (7)+(5+2)=14
Exactly! It's D
I got the answer AND I understand it! Thank you so much.