Answer:
shorter leg = 6 cm
Explanation:
let n be the shorter leg then n + 2 is the longer leg.
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
n² + (n + 2)² = 10² , that is
n² + n² + 4n + 4 = 100
2n² + 4n + 4 = 100 ( subtract 100 from both sides )
2n² + 4n - 96 = 0 ( divide through by 2 )
n² + 2n - 48 = 0 ← in standard form
(n + 8)(n - 6) = 0 ← in factored form
equate each factor to zero and solve for n
n + 8 = 0 ⇒ n = - 8
n - 6 = 0 ⇒ n = 6
However , n > 0 then n = 6
the shorter leg is 6 cm long