Question

The hypotenuse of a right angled triangle is $17$cm and the difference between the other two sides is $7$cm.Find the other two unknown sides.

Answer 1

Let one side be $x$cm.Since the difference between the two sides is $7$cm

$\therefore$ the other side$=x+7$cm

As the given triangle is a right angled triangle with hypotenuse $=17$cm

By using pythagoras theorem, we get

$x^2+{(x+7)}^2={17}^2$

$\Rightarrow x^2+x^2+14x+49-289=0$

$\Rightarrow 2x^2+14x-240=0$

$\Rightarrow x^2+7x-120=0$

$\Rightarrow x^2+15x-8x-120=0$

$\Rightarrow x(x+15)-8(x+15)=0$

$\Rightarrow (x+15)(x-8)=0$

$\Rightarrow x=-15$ or $x=8$

$x=-15$ cannot be negative

$\therefore x=8$

Hence the two sides of the triangle are $8$cm and $15$cm