The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm,

Now, since we have to find out base, let us assume the base to be ‘x’ cm.
Therefore the height of the triangle becomes ‘x −7’.

It is also given that the hypotenuse is 13 cm.
By Pythagoras Theorem,

$x^{2}+(x-7)^{2}=(13)^{2}$

$x^{2}+x^{2}+49-14 x=169$

$2 x^{2}-14 x-120=0$

$x^{2}-7 x-60=0$

Hence, this is our required quadratic equation.