Rectangle inscribed in a circle

[psm12se]

If a rectangle is inscribed in a circle of radius 5, is the area of the rectangle greater than 48

A. The ratio of the lengths of sides of the rectangle is 3:4

B. The difference between the lengths of sides of the rectangle is smaller than 3

[Uva@90]

If a rectangle is inscribed in a circle of radius 5, is the area of the rectangle greater than 48

A. The ratio of the lengths of sides of the rectangle is 3:4

B. The difference between the lengths of sides of the rectangle is smaller than 3

Hi Psm12se,

Here are few thing to note,
1) any Side of a rectangle can't be more than 10. since diameter is 10.
2) Side need not only be integers.
3) Diagonal of an inscribed rectangle is always the diameter of a circle.

To Find: IS Area > 48 (Yes/No Type)

Statement 1: l/b =The ratio of the lengths of sides of the rectangle is 3:4
so sides should be 6 and 8 (6^2+8^2 =100)
6*8 =48 !>48
Hence Sufficient.

Statement 2: The difference between the lengths of sides of the rectangle is smaller than 3

sides can be 6 and 8 (6^2+8^2 =100) 8-6 =2 <3 6*8 =48 =NO
Side can be 5sqrt(2) 5sqrt(2) (50+50=100): 0<3 50 >48 Yes
Hence In-sufficient.

Hence Answer is A

Regards,
Uva.

[psm12se]

Thanks for the reply.

OA is A but I choose answer as E because in this question, it is not stated explicitly that the vertices of the rectangle are on the circle.

[ceilidh.erickson]

OA is A but I choose answer as E because in this question, it is not stated explicitly that the vertices of the rectangle are on the circle.

I understand your concern, and it's good that you're thinking about alternative possible shapes. However, whenever the GMAT uses the word "inscribed" in a geometry question, it means that the vertices of one figure touch the sides of the other figure. A rectangle inscribed in a circle must have all of its vertices touching the circle.

[aashishagarwal]

Why the answers are hidden?

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Hi aashishagarwal,

As a 'courtesy' to people who are attempting this question, most other posters hide the correct answer choice from view (although if you scroll over the 'blacked-out' portion, you will be able to see the correct answer). This is so you don't 'accidentally' see the correct answer while you're reading through the prompt (or working on it).

GMAT assassins aren't born, they're made,
Rich