Given △QRS ≅△TUV , QS = 4w+16 and TV = 6w - 8, find the length of TV and QS. Show all the steps that you used to solve this problem in order to earn full credit.
Since △QRS ≅ △TUV, the corresponding sides are equal.
Therefore, we have:
QS = TV
4w+16 = 6w - 8
Rearranging the equation, we have:
4w - 6w = -8 - 16
-2w = -24
Dividing both sides by -2, we have:
w = -24/-2
w = 12
Therefore, the length of TV is:
TV = 6w - 8 = 6(12) - 8 = 72 - 8 = 64
And the length of QS is:
QS = 4w + 16 = 4(12) + 16 = 48 + 16 = 64
Therefore, the length of TV is 64 units and the length of QS is also 64 units.