Diameter of circle S... help!

the ratio between two diameters is sqrt(2) - rule 45`,45`,90` right triangle
radii will be different ine the same ratio of sqrt(2)
circle T has larger area than circle S, T(pi*r^2)/S(pi*r^2)=2

gmatpup wrote:The diameter of circle S is equal in length to a side of a certain square. The diameter of circle T is equal in length to the diagonal of the same square. The area of circle T is how many times the area of circle S?

A. squareroot 2
B. squareroot 2 +1
C. 2
D. pie
E. squareroot 2n

Anwswer is C


Please explain, thanks so much!!

Pick numbers. If the diameter for circle S is 4, the side of the square is also 4. The radius is 2 and the area is πr^2 = 4π.

Both sides of the square are 4 so the pythagorean theorem can be applied or as pemdas alluded to the 45, 45, 90 right triangle rule can be applied.

Pythagorean theorem - 4^2 + 4^2 = C^2. 16 + 16 = 32 = C^2. C = sqrt (32) = 4sqrt(2) = diameter of circle T. The radius for circle T is half of the diameter or 2sqrt(2). The area of circle T is (2sqrt(2))^2 * π = 4*2*π = 8π.

8Ï€ is two times 4Ï€.

Diameter of S=a
Diameter of T=2^1/2a[diagonal of the square]

so Area of T is twice the area of S