Question

If line ML is a midsegment of triangle IJK, find KJ

Answer 1

A midsegment connecting two sides of a triangle is parallel to the third side and is half as long.

$ML= \frac{1}{2}KJ \ \ \to \ \ KJ = 2ML = 2*12 = 24$

Answer 2

So what we're dealing with here is a similar triangle situation. Since ML is a midsegment, that means that IL and LJ are congruent. So, IL=LJ=13. This means that the whole side IJ is 26 (13+13=26). We also know that triangle IML and triangle IKJ are similar triangles, so their sides are proportional. This means that we can set up the ratio:
12/13 = x/26
and solve for x.
After multiplying 26 to both sides of the equation, we find that x=24, so KJ=24.