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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