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?25/4 pi is around 20. The area of inscribed rectangle cannot be more than this so it cannot be 24.
I do not have an answer to this question. How do we solve this?
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.
Ques1.jpg [ 7.04 KiB | Viewed 1671 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
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
Veritas Prep | GMAT Instructor
Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews