• # question_answer Which of the following forms a Pythagoras triplet? A) $(5,11,13)$ B) $(9,15,18)$ C) $(17,24,25)$ D) $(20,21,29)$

 According of Pythagoras theorem, ${{(\text{Longest side},\text{ i}.\text{e}.,\text{ hypotenuse)}}^{2}}$ $={{(\text{one side i}\text{.e}\text{.},\text{ base)}}^{2}}+{{(\text{other side i}\text{.e}\text{.},\text{ height)}}^{2}}$From option ; $(5,11,13)$ Longest side = 13, one side = 5 and other side = 11 Now, ${{(11)}^{2}}+{{(5)}^{2}}=121+25=146$ and       ${{(13)}^{2}}=169$ ${{(13)}^{2}}\ne {{(11)}^{2}}+{{(5)}^{2}}$ $(5,11,13)$ does not form a Pythagoras triplet. From option ; $(9,15,18)$ longest side =18, one side =9 and other side =15 Now,   ${{(15)}^{2}}+{{(9)}^{2}}=225+81=306$ and         ${{(18)}^{2}}=324$ ${{(18)}^{2}}\ne {{(15)}^{2}}+{{(9)}^{2}}$ $\therefore \,\,(9,15,18)$does not form a Pythagoras triplet. From option ; $(17,24,25)$ longest side =25, one side =17 and other side =24 Now,  ${{(17)}^{2}}+{{(24)}^{2}}=289+576=865$ and        ${{(25)}^{2}}=625$ ${{(25)}^{2}}={{(17)}^{2}}+{{(24)}^{2}}$ $\therefore \,(17,24,15)$ does not form a Pythagoras triplet. From option ; $(20,21,29)$ longest side =29, one side =21 and other side =20 Now, ${{(20)}^{2}}+{{(21)}^{2}}=400+441=841$ and ${{(29)}^{2}}=841$ ${{(29)}^{2}}={{(20)}^{2}}+{{(21)}^{2}}$ $\therefore \,(20,21,29)$ forms a Pythagoras triplet. So, option [d] is correct.