Question

The perimeter of a right triangle is 60 cm. Its hypotenuse is 26 cm . Find the other two sides and the area of the triangle .

Answer 1

$<b><u>Hello Friend!!!!</u></b>$


$\boxed{Merry \:Christmas}$


$Let \: a,b, c \:are\: the \:sides\: of \:a\: triangle .$


$Given\: that \: hypotenuse(c) = 26 \:cm.$


$a + b + c = 60\: cm.$


$\therefore a + b = 60 - c = 60 - 26 = a + b = 34 --------(1)$


$In\: a \:right\: angled \:triangle {c}^{2}  = {a}^{2}  + {b}^{2}$


${a}^{2}  + {b}^{2}  = {26}^{2}  = 676 ---------(2)$


$Now\: {a}^{2}  + {( 34 - a)}^{2}  = 676.  [ from (1)]$


$\implies {a}^{2}  + {a}^{2}  - 68a + 1156 = 676$


$\implies {2a}^{2}  - 34a + 480 = 0$


$\implies {a}^{2}  - 17a + 240 = 0$


$\implies {a}^{2}  - 10a - 24a + 240 = 0$


$\implies a(a - 10) - 24(a - 10) = 0$


$\therefore\: a = 10 , 24$


$but \:b = 34 - a \:then\: b = 24 , 10$


$\therefore\: sides\: of \:triangle \:are 10 , 24.$


$<b><u>Hope The Above Answer Helped.</u></b>$


$\mathbb{PLEASE \:MARK \:ME \:BRAINLIEST }$