Question

Can someone help? I cannot find in my book how to do this and and I can't find any further information online.
Given triangle QRS is congruent to triangle TUV, QS=3v+2 and TV=7v-6, find the length of QS and TV

Answer 1

\[\triangle{QRS} ≅ \triangle{TUV}
\\\text{Then} \space QS = TV
\\\text{Thus} \space 3v+2 = 7v - 6
\]

Solve for v

Answer 2

okay, what would be the first step? Would you first add the 2 and take away the 6?

Answer 3

or would you first try to get v on it's own?

Answer 4

Get your variable numbers on one side, and the normal numbers on the other

Answer 5

3v + 2 - 2 = 7v - 6 + 6

Answer 6

3v + 7v = 7v - 7v + 6

Answer 7

wait, messed that up

Answer 8

Then you would have 3v=7v if you cancel out each side right? But how do you go from there?

Answer 9

@seantay, don't confuse the poor guy

Answer 10

@Hero I was taught that you only cancel out/ add or take away with one of the numbers not both? Is it supposed to be ending up with 3v=7v?

Answer 11

3v + 2 = 7v - 6
2 + 6 = 7v - 3v
8 =4v
8/4 = v
2 = v

Length of QS = 3(2) + 2 = 8
Length of TV = 7(2) - 6 = 14 - 6 = 8

Answer 12

@Hero Thank you for your explanation, that matches what I have done in the past but I sometimes doubt if I am using the right way of solving a problem, I didn't know if there was a new way of solving this type of problem since it relates to congruence and angles.