Rectangle ABCD is inscribed in a circle with center X.

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AAPL: Moderator; Posts: 2749; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Tue Oct 02, 2018 2:59 am

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Veritas Prep

Rectangle ABCD is inscribed in a circle with center X. If the area of the rectangle is eight times its width, and the distance from X to side AB is three, what is the approximate circumference of the circle?

A. 5
B. 10
C. 30
D. 45
E. 75

OA C.

Source: Beat The GMAT — Problem Solving | Tue Oct 02, 2018 2:59 am

mongmat27: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Oct 02, 2018 5:16 am

by mongmat27 » Tue Oct 02, 2018 5:36 am

Ans is C - 30

Let length be a and width be b

Given - ab =8b

Thus, a=8

Thus, AB =8

Distance from centre to AB is 3. Let this line drawn from X (centre of circle) to AB meet AB at E. Thus, XE = 3

As X is the centre, XE will be perpendicular bisector to AB. Thus, EB = 4

Triangle EBX is a right angled triangles with one side =3 and other =4. Thus, the third side XB, which is the radius of the circle (because X is centre and B is a point on the circle) = 5 (Pythagoras theorem)

Thus, circumference = 2*3.14*5 = 31.4

option C is the closest approximation of 31.4

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Oct 03, 2018 4:58 pm

AAPL wrote:Veritas Prep

Rectangle ABCD is inscribed in a circle with center X. If the area of the rectangle is eight times its width, and the distance from X to side AB is three, what is the approximate circumference of the circle?

A. 5
B. 10
C. 30
D. 45
E. 75

Since the area of the rectangle is eight times its width, the length of the rectangle (AB or CD) is 8. Since the distance from X to side AB is 3, the distance from X to side CD is also 3. Therefore, AD or BC, that is, the width of the rectangle is 6. By the Pythagorean theorem, we have:

AC^2 = AB^2 + BC^2

AC^2 = 8^2 + 6^2

AC^2 = 100

AC = 10

Since AC is also the diameter of the circle, the circumference of the circle is AC x Ï€, or 10Ï€. Since Ï€ is approximately 3, the circumference is approximately 30.

Answer: C

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