If one leg of right triangle is 5cm shorter than the other leg The length of the hypotenuse is 25cm Find the length of the shorter leg?

Let the shorter leg be x-5 and the other leg be x.

Use Pythagoras' theorem:

(x-5)2+x2 = 625

(x-5)(x-5)+x2 = 625

2x2-10x+25 = 625

2x2-10x+25-625 = 0

2x2-10x-600 = 0

Solving the above using the quadratic equation formula works out as:

x = -15 or x = 20, so it must be the latter because dimensions can't be negative.

Therefore:the shorter leg is 15 cm