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The length of LN is 65.

Step-by-step explanation:

In MNK,

h² = p² + b²

or, 90² = 54²+b²

or, 8100 = 2916+b²

or, b² = 5184

so, b = 72

KN = 72

Now,

In LKN,

h²=p²+b²

or, 97²=LN²+KN²

or, 9409 = LN² + 72²

or, 9409 = LN² + 5184

or, LN² = 4225

so, LN = 65