Bisector of the right angle of a right-angled triangle, hypotenuse on from cutting lengths 15 cm

Bisector of the right angle of a right-angled triangle, hypotenuse on from cutting lengths 15 cm and 20 cm Find the lengths of the legs.

By the property of the bisector of a triangle, they divide the opposite side into segments proportional to the adjacent sides: AM / AC = BM / BC.

15 / AC = 20 / BC.

AC / BC = 3/4.

Let the length of the segment AC = 3 * X cm, then BC = 4 * X cm.

Hypotenuse AB = AM + BM = 15 + 20 = 35 cm.

Then, by the Pythagorean theorem, AB ^ 2 = AC ^ 2 + BC ^ 2.

1225 = 9 * X ^ 2 + 16 * X ^ 2.

X ^ 2 = 1225/25 = 49.

X = 7.

Then AC = 3 * 7 = 21 cm, BC = 4 * 7 = 28 cm.

Answer: The lengths of the legs are 21 cm, 28 cm.