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.

Answer 1

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.