Question

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

Answer 1

${AB}^2+{BC}^2={AC}^2$

(By pythagoras theorem)

$⟹{(x-7)}^2+x^2={13}^2$

$⟹x^2+x^2+49-14x=169$

$⟹2x^2-14x+(49-169)=0$

$⟹2x^2-14x-120=0$

$⟹x^2-7x-\frac{120}{2}=0$

$⟹x^2-7x-60=0$

$⟹x^2-12x+5x-60=0$

$⟹x(x-12)+5(x-12)=0$

$⟹(x-12)(x+5)=0$

$\therefore x=12$ (x=-5 is not possible since side can't be negative)

$\therefore Base=12cm$