What is The hypotenuse of a right triangle is 25 cm long One leg is 17 cm longer than the other Find the length of the shorter leg?

Apply Pythagoras

h^2 = l^2 + s^2

h = 25

l = s + 17

Substitute

25^2 = s^2 + ( s + 17)^2

625 = s^2 + s^2 + 34s + 289

Equating to zero

2s^2 + 34s - 336 =0

Divide by '2'

s^2 + 17s - 168 =0

Factor

( s + 24)(s - 7) = 0

Hence s = 7 (& s = -24 is unresolved).