Question

hypotenuse of a right angle triangle is 25 CM the long two sides are such that one is 5 cm is longer than other their length are

Answer 1

as we know that 
H²=P²+B²
25²=x²+(x+5)²
625=x²+x²+25+10x
625=2x²+10x+25

2x²+10x-600=0 

Answer 2

since the hypotenuse is 25cm, let the other two sides be x and x+5 respectively.
Therefore by Pythagorus theorem
x^2+(x+5)^2=25^2
x^2+x^2+10x+25=625. using (a+b)^2=a^2+2ab+b^2
2x^2+10x=625-25
2x^2+10x-600=0
2x^2+40x-30x-600=0
2x(x+20)-30(x+20)=0
(2x-30)(x+20)=0
therefore x=30/2=15 or x=-20
since the side of a triangle cannot be negative x=-20 is discarded
therefore the length of the other two sides are 15 and 20 respectively.
hope this helps