A right-angled triangle has its two perpendicular sides 6 cm and 12 cm long. A square is drawn inside it with two of its sides lying along those two perpendicular sides and its remaining corner touching the hypotenuse. Find the side of the square in cm.

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4. Place the right angle at the origin with the legs along the axes, reaching (12, 0) and (0, 6). The hypotenuse is x/12 + y/6 = 1. The free corner of the square is (s, s), so s/12 + s/6 = 1, i.e. 3s/12 = 1 and s = 4 cm.

A right-angled triangle has its two perpendicular sides 6 cm and 12 cm long. A square is drawn inside it with two of its sides lying along those two perpendicular sides and its remaining corner touching the hypotenuse. Find the side of the square in cm.

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