Question

perimeter of a right triangle is 40cm and its hypotenuse is 17cm find tha area of the triangle

Answer 1

$x + y + h = 40 \\ h = 17 \\ x + y = 40 - 17 = 23 \\ {x}^{2} + {y}^{2} = {17}^{2} \\ {x}^{2} + {(23 - x)}^{2} = 289 \\ {x}^{2} + 529 + {x}^{2} - 46x = 289 \\ 2 {x}^{2} - 46x + 240 = 0 \\ {x}^{2} - 23x + 120 = 0 \\ {x}^{2} - 15x - 8x + 120 = 0 \\ (x - 15)(x - 8) = 0 \\ sides \: are \: 15cm \: and \: 8cm \\ area \: = \frac{1}{2} \times 15 \times 8 = 60 {cm}^{2}$