| Direction: In the following questions, a question followed by two statements is given. You have to choose are out of the given five choices that answers the questions. |
| What is the length of a rectangle? |
| Statements: |
| I .The area of the rectangle is \[36\text{ }c{{m}^{2}}.\] |
| II. The sum of the length and breadth of the rectangle is 15 cm. |
A) Statement I alone is sufficient to answer the question while statement II alone is not sufficient to answer the question.
B) Both statements taken together are sufficient to answer the question, but either of them is not sufficient.
C) Either statement alone is sufficient.
D) Statement I and II together are not sufficient to answer the question and additional data is needed to answer the question,
E) Statement II alone is sufficient to answer the question.
Correct Answer: B
Solution :
Let the length be \[x\]metres. And the breadth be \[y\] metres. From I: Area \[=x\times y\] \[\therefore \]\[x\times y=36\,c{{m}^{2}}\] (i) From II:\[x+y=15\] ?(ii) From I and II, we get \[x-y=\sqrt{{{(x+y)}^{2}}-4xy}=\sqrt{225-4\times 36}\] \[=\sqrt{225-144}=\sqrt{81}=9\] \[\therefore \]\[x-y=9\] (iii) Solving (ii) and (iii), we have \[x+y=15\] \[\frac{x-y=9}{2x=24}\] \[\therefore \]\[x=12\] \[\therefore \]\[y=3\,c{{m}^{2}}\] Hence length = 12 cm
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