Median of Square's Area

Calculus Level 4

The length $$(L)$$ and width $$(W)$$ of a rectangle are random variables, independently and uniformly distributed on the interval $$[9,11],$$ and the area $$(A)$$ of the rectangle is also a random variable: $L,W \sim U(9,11);\ \ \ \ A = LW.$ It is not difficult to see that the expected value of the area is $$E[A] = 100.$$

Determine the median of the area.

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