Rectangle

[mmslf75]

Is the surface area of a rectangular pool larger than 1000 square feet?
(1) The pool measures fifty feet diagonally.
(2) One side of the pool measures twenty five feet.

OA is C

why noit A ?

[Lattefah84]

so what is OA?

I would say that both are sufficient together and neather is sufficient alone...

[ct799]

Does anybody have an answer-explanation why is C? I thought the maximum area on this case could be achieved by having the diagonal as a diagonal of a square?

any hints around???

[ajith]

Is the surface area of a rectangular pool larger than 1000 square feet?
(1) The pool measures fifty feet diagonally.
(2) One side of the pool measures twenty five feet.

OA is C

why not A ?

Say the sides of the rectangle are a and b

the area of the pool = a*b

1) sqrt(a^2+b^2) = 50
2) a = 25


1 is not sufficient, nor is 2

but combining 1&2 ,we can find out b and a*b hence C

[ajith]

Is the surface area of a rectangular pool larger than 1000 square feet?
(1) The pool measures fifty feet diagonally.

why noit A ?

the maximum area that a rectangle with diagonal measuring 50 feet is when it is square with side = 50/sqrt(2)

The area = side ^2 = 50*50/2 = 1250

It is above 1000 Sqft

had it been below 1000 we could have concluded that no pond can have area more than 1000 feet and we could have chosen A as sufficient.

[ say if the sides were sqrt(2450) and sqrt(50), the diagonal will be measuring 50 feet but the area is only sqrt(2 450) * sqrt(50) = 350 ]

[ct799]

ok smooth....i agree with you, thanks a lot for your help.