Question

The hypotenuse of a right=-angled triangle is 20 meters. If the difference between the lengths of the other sides be 4 meters, find the other sides 

Answer 1

Let one side of the right-angled triangle be x m and the other side be `(x+4)m` On applying Pythagoras theorem, we have: 

`20^2=(x+4)^2+x^2` 

⇒` 400x^2+8x+16+x^2` 

⇒ `2x^2+8x-384=0` 

⇒`x^2+4x-192=0` 

⇒`x^2+16x-12x-192=0` 

⇒ `x^2(x+16) -12(x+16)=0` 

⇒`(x+16) (x-12)=0` 

⇒` x=-16  or  x=12` 

The value of x cannot be negative.

Therefore, the base is 12 m and the other side is `{(12+4)=16m}`