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

To find the length of TV and QS, we can set up an equation based on the given information that △QRS is congruent to △TUV.

According to the congruence of the triangles, corresponding sides are equal, so we can set QS equal to TV:
QS = TV
4w + 16 = 6w - 8

To solve for w, we can simplify the equation:
4w + 16 = 6w - 8
16 = 2w - 8
24 = 2w
w = 12

Now that we have found the value of w, we can substitute it back into the expressions for QS and TV to find their lengths:
QS = 4w + 16
QS = 4(12) + 16
QS = 48 + 16
QS = 64

TV = 6w - 8
TV = 6(12) - 8
TV = 72 - 8
TV = 64

Therefore, the length of TV is 64 and the length of QS is 64.