| Directions: Each question consists of a question and two statements I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the questions. Read both the statements and choose the appropriate option. [IBPS (PO) 2014] |
| What is the base of a\[\Delta PQR\]and PQ as base? |
| I. Height and base of the triangle are in the ratio of 3: 4. |
| II. The area of the triangle is \[48\,\,c{{m}^{2}},\]perimeter \[36\,\,cm\] and height 2/3 of the perimeter. |
A) 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
B) The data either in statement I alone or in statement II alone are sufficient to answer the question
C) 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
D) The data in both statements I and II together are necessary to answer the question
E) The data even in both statements I and II together are not sufficient to answer the question
Correct Answer: A
Solution :
| From I, Base \[=4x,\]height \[=3x\] |
| Hence, we cannot determine the exact value of \[4x.\] |
| So, statement I atone is not sufficient to answer the question. |
| From II, Area of triangle \[=48\,\,c{{m}^{2}}\] |
| Now, \[\frac{1}{2}\times \text{Base}\times \text{Height}=48\] |
| \[\therefore \] \[\text{Base}\times \text{Height}=96\] (i) |
| Again, \[\text{Height}=\frac{2}{3}\times \text{Perimeter}=\frac{2}{3}\times 36=24\,\,cm\] |
| Now, from Eq. (i), we get \[\text{Base}\times 24=96\] |
| \[\therefore \] Base \[=4\,\,cm\] |
| Hence, statement II alone (s sufficient to answer the question. |
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