Given QRS=TUV, QS=3v+2 and TV=7v-6, find the length of QS and TV
Since QRS=TUV, we know that QS + ST + TR + RV = QS + TV.
We are given that QS = 3v + 2 and TV = 7v - 6.
Plugging in these values, we get:
(3v + 2) + ST + TR + (7v - 6) = (3v + 2) + (7v - 6).
Simplifying the equation, we have:
3v + 2 + ST + TR + 7v - 6 = 3v + 2 + 7v - 6.
Combining like terms, we get:
10v - 4 = 10v - 4.
Since the two sides of the equation are already equal, we can solve for ST + TR:
ST + TR = 0.
This means that ST = -TR. Since these two segments are equal, they must both be 0.
Therefore, the length of QS is 3v + 2, and the length of TV is 7v - 6.