Question

Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is longer than the other by 5 cm. Find the lengths of the other two sides

Answer 1

let one side be x cm
then another side =(x+5)cm
x^2+(x+5)^2=(25)^2
x^2+x^2+10x+25=625
2x^2+10x-600=0
x^2+5x-300=0
x^2+20x-15x-300=0
x(x+20)+15(x+20)=0
(x+20)(x-15)=0
according to this x may be -20 or 15
as we know that the length of the sides must be positive so 
one side =15cm
other side=(x+5)=(15+5)=20 cm

Answer 2

Let one side be x cm

then another side =(x+5)cm

x^2+(x+5)^2=(25)^2

x^2+x^2+10x+25=625

2x^2+10x-600=0

x^2+5x-300=0

x^2+20x-15x-300=0

x(x+20)+15(x+20)=0

(x+20)(x-15)=0

As we know that the length of the sides must be positive so 

one side =15cm

other side=(x+5)=(15+5)=20 cm