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

Question:

The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, form the quadratic equation to find the base of the triangle.

Solution:

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.