[SBI (Management Executive) 2014] Find the radius of the semi-circle. I. The area of semi-circle is equal to the area of the rectangle. II. The breadth of rectangle is 5 cm less than its length and its perimeter is 50 cm.
A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
C) If the data either in statement I alone or in statement II alone are sufficient to answer the question
D) If the data given in both the statements I and II together are not sufficient to answer the question
E) If the data in both the statements I and II together are necessary to answer the question
Correct Answer: E
$ \therefore $ $ 2(x+x-5)=50 $
$ \Rightarrow $ $ 2x-5=25 $
$ \Rightarrow $ $ 2x=25+5=30 $
$ \Rightarrow $ $ x=15cm=Length $
$ \therefore $ Breadth $ =15-5=10cm $ From I, $ \frac{\pi r^{2}}{2}=15\times 10 $
$ \Rightarrow $ $ \pi r^{2}=300 $
$ \Rightarrow $ $ r=\sqrt{\frac{300}{\pi }} $
Hence, both statements I and II are required.
BETA
