The hypotenuse of a right triangle is 10cm long. The longer leg is 2cm longer than the shorter leg. Find the side lengths of the triangle.

Length of the shorter leg: __cm

Length of the longer leg: __cm

Length of the hypotenuse: __cm

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