| Which of the following are not the sides of a right angled triangle? [SSC (CGL) 2014] |
A) \[3,\] \[4,\] \[5\]
B) \[1,\]\[1,\]\[\sqrt{2}\]
C) \[1,\]\[\sqrt{3},\]\[2\]
D) \[\sqrt{3},\]\[\sqrt{4},\]\[\sqrt{5}\]
Correct Answer: D
Solution :
| We know that, the sides of right angle triangle always follow Pythagoras theorem, |
| i.e. \[{{\text{(Hypotenuse)}}^{\text{2}}}\text{=(1st}\,\,\text{side}{{\text{)}}^{\text{2}}}\text{+(2nd}\,\,\text{side}{{\text{)}}^{\text{2}}}\] |
| 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. |
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