We need Pythagoras theorem here a^2+b^2 = c^2 a, b = legs of a right-triangle c = length of hypotenuse
Let S=shorter leg, in cm, then longer leg=S+2 cm use Pythagoras theorem S^2+(S+2)^2 = (10 cm)^2 expand (S+2)^2 S^2 + S^2+4S+4 = 100 cm^2 [collect terms and isolate] 2S^2+4S = 100-4 = 96 cm^2 simplify and form standard form of quadratic S^2+2S-48=0 Solve by factoring (S+8)(S-6) = 0 means (S+8)=0, S=-8 or (S-6)=0, S=6 Reject nengative root, so Shorter leg = 6 cm Longer leg = 6+2 cm = 8 cm Hypotenuse (given) = 10 cm
