A triangle has sides of 18cm and 32cm. The measurement of the longest side is missing. Ted says that one possibility for the unknown side is 47cm. Do you agree with Ted? Why or why not?

Since the measurement of the longest side is missing we can use the pythagorean theorem to find the hypotenuse or longest side.

18^2 + 32^2 = c (hypotenuse) ^2
324 + 1,024 = c^2
1,348 = c^2
sqrt 1,348 = c
36.72 = c
i do not agree with ted because when you use the pythagorean theorem you do not get 47cm

this can be proved by
18^2 + 32 ^2 = 47^2
we already know the left side is 1,348
1,348 = 47^2
1,348 does not equal 2,209 which is 47 squared