In a right-angled triangle, the legs are 21 and 28. Find the lengths of the segments into which the hypotenuse

In a right-angled triangle, the legs are 21 and 28. Find the lengths of the segments into which the hypotenuse is divided by the bisector of the right angle.

Let us determine the length of the AC hypotenuse using the Pythagorean theorem.

AC ^ 2 = BC ^ 2 + AB ^ 2 = 28 ^ 2 + 21 = 784 + 441 = 1225.

AC = 35 cm.

Let the length of the segment AH = X cm, then the length of the segment CH = (35 – X) cm.

The bisector of the angle of the triangle divides the opposite side into segments proportional to the adjacent sides, then: AC / AH = BC / CH.

21 / X = 28 / (35 – X).

28 * X = 21 * (35 – X).

49 * X = 735.

X = AH = 735/49 = 15 cm.

CH = 35 – 15 = 20 cm.

Answer: The lengths of the segments are 15 cm and 20 cm.