Median MH is 6 units longer than median KP triangle GHI is similar to triangle JKL. If GH:JK=7:5, find the length of KP

If GHI and JKL are similar with the proportion of 7/5 (reduction), that means all the elements of GHI & JKL have the same reduction ratio (median, Altitude, etc.)

Then HM/KP = 7/5. But we are given that HM = KP+6, so:

(KP+6) / KP = 7/5. Now cross multiplication:

5 (KP+6) = 7KP

5KP + 30 = 7KP

30 = 2KP and KP = 15