BTGmoderatorDC wrote: ↑

Wed Jun 10, 2020 5:56 pm

Q3_Img.png

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: Veritas Prep

Since the distance from center X to side AB is 3, and the distance from X to side AB is perpendicular to AB, the perpendicular would be parallel to the width of the rectangle ABCD and equal to 2*3 = 6 units

Again, we know that the area of the rectangle is eight times its width (6), the length of the rectangle would be 8.

Say the perpendicular from X to AB bisects AB at point Y; thus, YB = 8/2 = 4, XY = 3 and ∆XYB is a rightangled ∆.

By Pythagoras theorem, we have XB^2 = Radius^2 = XY^2 + YB^2 = 3^2 + 4^2 = 25

=> XB = Radius = r = √25 = 5

The circumference of the circle = 2πr = 2*3.14*5 = 31.4 = ~30 units

The correct answer: C

Hope this helps!

-Jay
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