swerve wrote:
In the figure above, \(ABCD\) is a rectangle. What is the area of the semi-circular region with center \(O\) and diameter \(BC\)?
1) \(\frac{BC}{AB}=\frac{3}{4}\)
2) \(BD=25\)
The OA is
C
Source: Manhattan Prep
To get the area, we must know either BO or BC.
Let's take each statement one by one.
1) \(\frac{BC}{AB}=\frac{3}{4}\)
Ratio value can't help as it would not render a unique answer. Insufficient.
2) \(BD=25\)
Can't get BC with the help of BD. Insufficient.
(1) and (2) together
From (1), say BC = 3x and AB = CD = 4x
Since ABCD is a rectangle, ∆BCD is a right-angled triangle.
Thus, BC^2 + CD^2 = BD^2
(3x)^2 + (4x)^2 = (25)^2
=> x = 5 => CD = 15. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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