smitakokne wrote:

The area of a rectangle inscribed in a circle is 24. Area of the circle is 25/4 pi. What is the perimeter of the rectangle?

I do not have an answer to this question. How do we solve this?

25/4 pi is around 20. The area of inscribed rectangle cannot be more than this so it cannot be 24. From the way this question is formed, I would expect the area of the rectangle to be 12. (I will explain this later). I will solve the question assuming this value of area.

Area of circle = 25/4 pi = pi*r^2

Radius of circle = 5/2 and diameter is 5.

The rectangle inscribed in the circle will have its center at the center of the circle since its opposite sides are equal and parallel. The diagram below will show you why it should be so.

Attachment:

Ques1.jpg [ 7.04 KiB | Viewed 4148 times ]
So diameter of the circle should be the diagonal of the rectangle i.e. 5.

So area of rectangle = ab = 12

and \(a^2 + b^2 = 5^2\) (pythagorean theorem)

The most common pythagorean triplet is 3,4,5 and since the diagonal was 5, I was looking for the sides to be 3 and 4 possibly giving the area as 12. In GMAT, numbers fall in place very well)

Sides must be 3 and 4 giving the perimeter as 2(3+4) = 14

_________________

Karishma

Veritas Prep GMAT Instructor

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