Question

Given △QRS ≅△TUV%0D%0A△%0D%0A%0D%0A%0D%0A%0D%0A %0D%0A≅%0D%0A△%0D%0A%0D%0A%0D%0A%0D%0A, 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 need to set up an equation using the given information.

From the congruence of triangles △QRS ≅ △TUV, we can conclude that the corresponding sides of both triangles are equal. Therefore, we have:

QS = TU (corresponding sides are equal)
4w + 16 = 6w - 8 (substituting the given expressions for QS and TV)

Next, we solve the equation for w:

4w + 16 = 6w - 8 (subtracting 4w from both sides to isolate the w term)
16 = 2w - 8 (adding 8 to both sides)
24 = 2w (dividing both sides by 2)
w = 12

Now that we know 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 QS is 64 and the length of TV is also 64.