Find the hypotenuse of a right-angled triangle, whose height drawn to the hypotenuse = 6√3 cm

Find the hypotenuse of a right-angled triangle, whose height drawn to the hypotenuse = 6√3 cm, and the projection of one from the legs to the hypotenuse = 60 cm

Let’s introduce the following designations: с – hypotenuse; a and b – legs; ca and cb are the projections of the respective legs onto the hypotenuse; h is the height drawn from the vertex of the right angle of this right-angled triangle.
The theory says: “The height of a right-angled triangle, drawn from the vertex of the right angle, is equal to the geometric mean of the projections of the legs onto the hypotenuse: ca * cb = h ^ 2.
For our example, h = 6√3 cm, ca = 60 cm.Therefore, (60 cm) * cb = (6√3 cm) 2, whence cb = (108 cm2): (60 cm) = 1.8 cm …
It is clear that c = ca + cb = 60 cm + 1.8 cm = 61.8 cm.
Answer: 61.8 cm.