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Given ΔQRS≅ΔTUV
, QS=3v+2
and TV=7v−6
, find the length of QS and TV.
(2 points)
Since ΔQRS≅ΔTUV, we know that the corresponding sides of the two triangles are congruent. Therefore, we have:
QS = TV
To find the length of QS and TV, we need to set up an equation using the given information.
Given: QS = 3v + 2 and TV = 7v - 6
Setting up the equation:
3v + 2 = 7v - 6
Now we solve for v:
2 + 6 = 7v - 3v
8 = 4v
Dividing both sides by 4:
v = 2
Now that we have found the value of v, we can substitute it back into the equations to find the length of QS and TV.
QS = 3v + 2 = 3(2) + 2 = 6 + 2 = 8
TV = 7v - 6 = 7(2) - 6 = 14 - 6 = 8
Therefore, the length of QS is 8 and the length of TV is also 8.