A level maths statistics question

Rectangles with perimeter of 40cm are produced randomly. The length, in cm, of the shorter side, X, is uniformly distributed across all possible values of X.
a) state the mean and variance of X (3 marks)
b) find the probability that the area of a rectangle is greater than 96cm^2 (5 marks)

Can you start the question, so what would the range of values that X could take, then what would be the mean ....

The mean is 5 and the variance is 25/3, but I do t know how to do part (b)

What would be the range of values that the shorter side could take for that area?

Idk tbh

Its really basic algebra/area rather than probability so assume the shorter side is x, then the longer side is ... and the area is .... and this is greater than 96 when ...

I don’t understand how to get the longer side though

The perimeter is 40. Its a rectangle.

Okay i think I kinda understand it now, sorry.
Thank you

You should have come across this type of problem before as its a classic greek one where the aim is to maximise the area of a rectangle (obv the answer is a square) given that the perimeter is fixed which generates a quadratic ...