Step-by-step explanation:
geometric mean theorem :
h = sqrt(p×q)
h being the height on the Hypotenuse in a right-angled triangle, p and q being the 2 line segments the height splits the Hypotenuse into.
so,
n = sqrt(6×24) = sqrt(144) = 12
m we get now via Pythagoras
m² = 6² + 12² = 36 + 144 = 180
m = sqrt(180) = sqrt(4×9×5) = 2×3×sqrt(5) = 6×sqrt(5)
