In a right-angled triangle, the bisector of an acute angle divides the leg into segments of length 20 cm

In a right-angled triangle, the bisector of an acute angle divides the leg into segments of length 20 cm and 12 cm. Calculate the perimeter of the triangle.

Since BD is the bisector of the angle, it divides the AC leg into segments proportional to the adjacent sides.

BC / AB = CD / AD = 12/20 = 3/5.

Let BC = 3 * X cm, then AB = 5 * X cm.

Leg length AC = CD + AD = 12 + 20 = 32 cm.

By the Pythagorean theorem, AC ^ 2 = AB ^ 2 – BC ^ 2.

1024 = 25 * X ^ 2 – 9 * X ^ 2 = 16 * X ^ 2.

X ^ 2 = 1024/16 = 64.

X = 8.

Then BC = 3 * 8 = 24 cm, AB = 5 * 8 = 40 cm.

Let’s define the perimeter of the triangle ABC.

Ravs = 32 + 24 + 40 = 96 cm.

Answer: The perimeter of the triangle is 96 cm.