Question

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

Answer 1

Answer: KP=15

Explanation:

HM/KP = 7/5.

HM = KP+6, so:

(KP+6)/KP =7/5.

cross multiply

5(KP+6) = 7KP

5KP + 30 = 7KP

30 = 2KP and KP = 15

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Answer 2

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