Question

The height of a right triangle is $7$ cm less than its base. If the hypotenuse is $13$ cm, the quadratic equation to find the base of the triangle is $x^2-7x-60=0$

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ Let the base $BC$ of the right triangle be $xcm$

$\therefore$ Altitude $=AB=(x-7)cm$

$\Rightarrow$ Hypotenuse $=AC=13cm$

According to Pythagoras theorem,

$\Rightarrow$ $(AC{)}^2=(AB{)}^2+(BC{)}^2$

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

$\Rightarrow$ $169=x^2+49-14x+x^2$

$\Rightarrow$ $169=2x^2-14x+49$

$\Rightarrow$ $2x^2-14x-120=0$

$\therefore$ $x^2-7x-60=0$