The hypotenuse of a right-angled triangle is 25 cm, and the height drawn to it is 12 cm.

The hypotenuse of a right-angled triangle is 25 cm, and the height drawn to it is 12 cm. Find the legs of the triangle and the segments by which the hypotenuse is divided by the height drawn to it.

X – one segment of the divided hypotenuse
25 – x – second segment
x² + 12² – square of one leg
(25 – x) ² + 12² – the square of the other leg
The square of the hypotenuse is equal to the sum of the squares of the legs:
25² = x² + 12² + (25 – x) ² + 12²
625 = x² +144 + 625 – 50x + x² + 144
2x² – 50x + 288 = 0 ⇒x² – 25x + 144 = 0, x = 16, x = 9
If x = 16 cm, then the second segment is – 9 cm
√16² + 12² = √400 = 20 cm – one leg
√9² + 12² = √225 = 15 cm – second leg