Answer:
22.5
Explanation:
first of all, the first sign in the designations of the triangles is not an A. it is the Greek Delta (capital) sign. standing for "triangle" due to its shape.
as the diagram shows (and the description says correctly), ADL and AKM are similar triangles.
that means they have the same angles.
and in order to keep the same angles even when the lengths of the sides are different, the relative relation of the side lengths must be the same for all sides.
that means, if one side changes by a factor f, then both other sides must change by the same factor.
so, by checking the change factor for AD (to AK), we can then determine the change of AL to AM. and then we simply subtract AL from AM and get LM.
the original AD = 14.
AK = AD + DK = 14 + 21 = 35
the change factor f is then AK/AD = 35/14 = 5/2
in other words AD grew by a factor of 5/2.
AM is then created by applying the same factor to AL.
=> AM = 15 * 5 / 2 = 75 / 2 = 37.5
=> LM = AM - AL = 37.5 - 15 = 22.5