Question: Which of the following are not the sides of a right angled triangle?
Options:
A) $ 3, $ $ 4, $ $ 5 $
B) $ 1, $ $ 1, $ $ \sqrt{2} $
C) $ 1, $ $ \sqrt{3}, $ $ 2 $
D) $ \sqrt{3}, $ $ \sqrt{4}, $ $ \sqrt{5} $
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Answer:
Correct Answer: D
Solution:
- We know that, the sides of right angle triangle always follow Pythagoras theorem,
i.e. $ {{\text{(Hypotenuse)}}^{2}}\text{=(1st}side{{)}^{2}}\text{+(2nd}side{{)}^{2}} $
By hit and trial method,
From option [a],
$ {{(5)}^{2}}={{(3)}^{2}}+{{(4)}^{2}} $
$ \Rightarrow $ $ 25=9+16=25 $
Hence, option [a] contains sides of right angled triangle.
From option [b]
$ {{(\sqrt{2})}^{2}}={{(1)}^{2}}+{{(1)}^{2}} $
$ \Rightarrow $ $ 2=1+1=2 $
Hence, option [b] contains sides of right angled triangle.
From option [c]
$ \Rightarrow $ $ {{(2)}^{2}}={{(1)}^{2}}+\sqrt{{{(3)}^{2}}} $
$ \Rightarrow $ $ 4=1+3=4 $
Hence, option [c] contains the sides of right angled triangle.
From option [d],
$ \Rightarrow $ $ {{(\sqrt{5})}^{2}}={{(\sqrt{3})}^{2}}+{{(\sqrt{4})}^{2}} $
$ \Rightarrow $ $ 5\ne 3+4=7 $
Hence, option [d] does not contains the sides of right angled triangle.
BETA
