Question

The altitude of right triangle is 7 cm less than its base. If, hypotenuse is 13 cm. Find the other two sides​

Answer 1

Let x be the base of the triangle, then the altitude will be (x−7).

By Pythagoras theorem,

x^2+(x−7)^2=(13)^2

2x^3−14x+49−169=0

2x^2−14x−120=0

x^2−7x−60=0

x^2 −12x+5x−60=0

(x−12)(x+5)=0

x=12,x=−5

Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and the altitude of the triangle will be 12−7=5cm.