Data Sufficiency

In rectangle ABCD, the length of the diagonal is 5 cm. what is the area of the rectangle ?

1) The rectangle ABCD is inscribed in a circle and it circumscribes another circle.

2)Of all the possible rectangles with a diagonal 5 cm long, rectangle ABCD has the maximal perimeter.

help..

don't have the answer..

Hi,

Thanks for the interesting question.

Stmt 1:

The rectangle ABCD is inscribed in a circle - A redundant statement - Every rectangle is a cyclic.

The rectangle circumscribes another circle - An inner circle (such that each of the sides is a tangent) could be drawn one and only if the rectange is a square. Now, that we know that it is a square whose diagonal is 5 cms long, one can find out the area. Hence, sufficient.

Stmt 2:

For a given diagonal, the rectangle will have the maximum perimeter when it is a square. Now, that we know that it is a square whose diagonal is 5 cms long, one can find out the area. Hence, sufficient.

Hence, answer is D.

Nowhere, do we actually need to find out the area of the square. As long we know that it can be calculated, we can leave it at that.

Hope this helps. Thanks.

my problem is the word "rectangle"
by defenition the diagonals in a rectangle are not perpendicular to each other..

samirkl wrote:my problem is the word "rectangle"
by defenition the diagonals in a rectangle are not perpendicular to each other..

In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. it does not have any specification for diagonals.
Also square is a special case for rectangle where all four side are equal.