Plz help me out?

Question

The sides of a rectangle are chosen at random each less than a given length 'a',all such lengths being equally likely.Find the probability that the diagonal is less than 'a'.

Answer 1

1/4 pi

Draw a square, the sides of which have length 'a'. The random rectangle can be "constructed" in this square, with one corner (say the lower left corner) coincident with the corner of the square. The opposite corner of the rectangle is somewhere in the square. For the diagonal to measure less than 'a', that corner must be inside a quarter-circle centered at the lower left corner, with radius 'a'. Compare the areas of the quarter-circle and the square.

By the way, 1/4 pi is about 0.7854

Answer 2

the probability of the diagonal having a diAGONAL less than a is 0. This goes against the pythagorac theorem.If a rectangle is divided into 2 triangles(keeping the diagonal as one side) then it can be found that the diagonal(or the hypotenuse of the triangle) is found by the formula A^2 + B^2 = c^2.Which will always be greater than the length a

Answer 3

let l= length, where l Let w = width, where w Thus l^2 +w^2 < 2a^2
The diagonal d is given by d^2 = l^2 +w^2
Therefore d^2 < 2a^2
d < a* Sqrt(2)
Hence d will always be less than a so the probability is 1 or 100%.

Answer 4

Mathematics infinety
Phycics Limited

Answer 5

its the easiest sum ever done.
Probability of the given event i.e. P(E) = no. of possible outcome/ no.of total favourable outcomes.
there the answer is a/4

Answer 6

if length of rectangle is a then length of its digonal is a*underrute2. and if length of digonal is a then side is a/underrute2. so probablity of having digonal less than a is 1/underrute2.

Answer 7

i would love to help but i dont under stand