SOLUTION: a point P is randomly chosen in the line AB of length 2a.what is the probability that the area of the rectangle having sides AP and PB will exceed a^2/2?

Question 1030260: a point P is randomly chosen in the line AB of length 2a.what is the probability that the area of the rectangle having sides AP and PB will exceed a^2/2?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let x be such that . Then the adjacent sides of the rectangle would have sides x and 2a - x. (Why?)
The area of the rectangle would be .
The area under the curve is given by square units.
==> The cdf for the area is given by .
Now solve for the bounds on x that will give a rectangular area of :

<==> after simplifying.
==> , .
==>
=.
This is approximately equal to to five significant figures.
RELATED QUESTIONS
In rectangle ABCD, AB=10 and BC=15. A point P inside the rectangle is such that BP=12,... (answered by mananth,ikleyn)

Find the odds against a randomly chosen household having a cat if the probability of the... (answered by stanbon)

If a point is randomly chosen on the square shown, what is the probability that it will... (answered by Fombitz)

Here is the probability model for the blood type of a randomly chosen person in the... (answered by ewatrrr)

Here is the probability model for the blood type of a randomly chosen person in the... (answered by Theo)

In the figure... (answered by stanbon)

The area of the rectangle is 2a^2+13a-24. If the length of the rectangle is given as... (answered by josgarithmetic)

Say that a randomly chosen individual can identify the professor with probability 0.68.... (answered by stanbon)

Say that a randomly chosen individual can identify the professor with probability 0.47.... (answered by stanbon)