3 years ago

Pentagons STUVW and XYZAB are similar with XY = 32 , YZ = 36 , ST = 4c + 2 and TU = 5c + 2 What is the length of TU

Mathematics

1 answer:

Vesna [10]3 years ago

8 0

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

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