Question

12. The sides of a right triangle containing the right angle are (5x) cm and (3x - 1) cm. If the
area of the triangle be 60 cm² ?, calculate the length of the sides of the triangle.
​

Answer 1

PROCESS

The area of the right angled triangle is

$\frac{1}{2} \times base \times height \\ here \\ \frac{1}{2} \times 5x \times (3x - 1) = 60 \\ 15 x{}^{2} - 5x = 120 \\ 3x {}^{2} - x - 24 = 0 \\ 3x {}^{2} - 9x + 8x - 24 = 0 \\ 3x(x - 3) + 8(x - 3) = 0 \\ (x - 3)(3x + 8) = 0 \\ either \: \: (x - 3) = 0 = > x = 3 \\ or \: \: (3x + 8) = 0 = > x = - \frac{8}{3} \\ now \: xcan \: not \: be \: nagetive \: as \: this \: is \: the \: side \: of \: the\: trinagle \\ \: and \: the \: side \: or \: length \: can \: not \: be \: zero \\ so \: x = 3 \: is \: taken \: in \: cosideration$

ANSWERS

THE LENGHTS ARE (5×3)=15cm ,(3×3-1)=8 cm

and hypotenuse=√(15^2+8^2)=17 cm