Question

Geometry: If segment JK measures 12 feet and segment JM is congruent to segment KM, what is the approximate length of segment JM? http://i44.tinypic.com/wpgyq.png
I disagree with the answer key and trying to make sure I'm not going crazy.

Answer 1

JKL is an isosceles triangle with congruent sides JK and KL
JK = 12 ft, so KL = 12 ft

The measure of JM would be 1/2 of JL, because KM is perpendicular to JL (given) and KM extends from the vertex angle of the isosceles triangle JKL to the base, making it a perpendicular bisector to JL
JM = 1/2 (JL)

We can find the length of JL by Pythagorean Theorem (a^2 + b^2 = c^2
JK^2 + KL^2 = JL^2
12^2 + 12^2 = JL^2
288 = JL^2
12sqrt(2) = JL

JM = 1/2 (12 sqrt(2))
JM = 6 sqrt(2)
~ 8.5 (8.48528...)

Answer 2

by pythagoras
12^2 = 2 JM^2 (since JM = KM)

jm = sqrt72 = 8.5 approx

Answer 3

that works too, and is a lot less work lol

Answer 4

thank you both