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.