The altitude of a right triangle is 7 cm less than its base. If the Hypotenuse is 13 cm, find the other two sides. [ncert 10th]

Let the base of the given rt|_d triangle=x cm.

Then its altitude = x-7 cm.

[Here Altitude=Height=perpendicular length] 

Hypotenuse = 13 cm.

Now in right-angled triangle, 

(Hypotenuse)²=(Based)²+(Altitude)²

=> (13)²=x²+(x-7)²

=> 169=x²+x2+49-14x

=> 2x²+49-14x-169=0

=> 2x²-14x-120=0

Dividing both sides by 2, we get,

x²-7x-60=0

=> x²-12x+5x-60=0

=> (x²-12x)+(5x-60)=0

=> x(x-12)+5(x-12)=0

=> (x-12)(x+5)=0

=> x=12, -5

But length of a side of a triangle cannot be negative. So x=12

=> Base=12 cm. Ans.

Altitude=x-7=12-7=5cm. Ans.