Answer:
TU = 4.5units
Step-by-step explanation:
Since the pentagons are similar, hence the ratios of their similar sides will be equal to a constant.
Hence;
XY/ST = YZ/TU
Given the following
XY = 32
YZ = 36
ST = 4c + 2
TU = 5c + 2
Substitute into the expression as shown;
32/4c+2 = 36/5c+2
Cross multiply
36(4c+2) = 32(5c+2)
144c + 72 = 160c + 64
144c - 160c = 64 - 72
-16c = -8
c = -8/-16
c = 1/2
Recall that TU = 5c + 2
TU =5(1/2) + 2
TU = 2.5 + 2
TU = 4.5
Hence the length of TU is 4.5units
