Question

ABCDEF is congruent to PQRSTU in the figure below. They represent the bases of two fountains.

Two six sided polygons ABCDEF and PQRSTU are drawn. AF makes an obtuse angle with FE at F. BC makes an obtuse angle with CD at C. PU makes an obtuse angle with UT at U. QR makes an obtuse angle with RS at R. Measures of sides of ABCDEF are : AB is 12 feet, BC is 18 feet, CD is 18 feet, DE is 12 feet, FA is 20 feet.

If the total length of the brick edge for each fountain is 100 feet, what is the length of side TU?

Answer 1

fill in the given info and let EF = x

Answer 2

because ABCDEF = PQRSTU, this means that EF = TU by the CPCTC property

Answer 3

oh the actual pic doesn't matter, what really matters is that we can see that EF = TU

Answer 4

and realize that the sides of ABCDEF add up to 100

Answer 5

ok so they are the same

Answer 6

so if the sides of ABCDEF add up to 100, then

AB + BC + CD + DE + EF + FA = 100

12+18+18+12+x+20 = 100


now solve for x

Answer 7

20

Answer 8

x=20

Answer 9

good, so EF = 20 and TU = 20