Question

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

Answer 1

ST = 4

Explanation:

If the pentagons are similar, the ratio between a pair of sides of one pentagon is the same ratio for the similar pair of sides of the second pentagon, so we have that:

XY / YZ = ST / TU

32 / 36 = (4c + 2) / (5c + 2)

8 / 9 = (4c + 2) / (5c + 2)

8*(5c + 2) = 9*(4c + 2)

40c + 16 = 36c + 18

4c = 2

c = 0.5

So the length of ST is:

ST = 4c + 2 = 4*0.5 + 2 = 4