Quantitative Aptitude Ques 2381
Question: Consider the following statements
I. Let ABCD be a parallelogram which is not a rectangle. Then, $ 2,(AB^{2}+BC^{2})\ne AC^{2}+BD^{2} $ II. If ABCD is a rhombus with AB = 4 cm, then $ AC^{2}+BD^{2}=n^{3} $ for some positive integer n. Which of the above statements Ware Correct?
Options:
A) Only I
B) Only II
C) Both I and II
D) Neither I nor II
Show Answer
Answer:
Correct Answer: B
Solution:
- I. ABCD is a parallelogram, then $ AC^{2}+BD^{2}=2,(AB^{2}+BC^{2}) $ II. ABCD is a rhombus and diagonals AC and BD bisect each other.
$ \therefore $ $ AO=OC $ and $ OB=OD $ In $ \Delta AOB, $ $ AB^{2}=AO^{2}+OB^{2} $
$ \Rightarrow $ $ {{(4)}^{2}}={{( \frac{AC}{2} )}^{2}}+{{( \frac{BD}{2} )}^{2}} $
$ \therefore $ $ AC^{2}+BD^{2}=64={{(4)}^{3}} $ i.e. $ n^{3} $
BETA
