Triangle QRS is congruent to Triangle TUV, QS = 3v+2 and TV = 7v-6, find the length of QS and TV.
Show your work please
Given that Triangle QRS is congruent to Triangle TUV, we can conclude that the corresponding sides are congruent.
Let's assign a variable to one of the sides.
Let's say QS is x.
According to the information provided, QS = 3v + 2.
Substituting x for QS, we have:
x = 3v + 2
Now, using the information that Triangle QRS is congruent to Triangle TUV, we know that TV is also x.
Given that TV = 7v - 6, we have:
x = 7v - 6
Since x = QS and x = TV, we can equate the two expressions for x:
3v + 2 = 7v - 6
Let's solve for v:
3v - 7v = -6 - 2
-4v = -8
v = -8 / -4
v = 2
Now that we know v = 2, we can substitute this value back into the expressions for QS and TV to find their lengths.
QS = 3v + 2
QS = 3(2) + 2
QS = 6 + 2
QS = 8
TV = 7v - 6
TV = 7(2) - 6
TV = 14 - 6
TV = 8
Therefore, the length of QS is 8 and the length of TV is also 8.