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.

Answer 1

Let the base of the right triangle be x cm.
Its altitude = (x−7) cm
From Pythagoras theorem, we have
$Bas{e}^2$+$Altitud{e}^2$=$Hypotenus{e}^2$

∴$x^2$+(x−7)2=132
⇒$x^2$+x2+49−14x=169
⇒2$x^2$−14x−120=0
⇒$x^2$−7x−60=0
This is the required quadratic equation. This can be solved using splitting the middle term method to find out the value of x
⇒$x^2$−12x+5x−60=0
⇒x(x−12)+5(x−12)=0
⇒(x−12)(x+5)=0
Either x−12=0 or x+5=0,
⇒x=12 or x=−5
Since sides are positive, x can only be 12.
Therefore, the base of the given triangle is 12 cm and the altitude of this triangle will be (12−7) cm=5 cm.