The 2 sides of the triangle are 20 and 30 cm, and the bisector of the angle between them divides the third side into segments

The 2 sides of the triangle are 20 and 30 cm, and the bisector of the angle between them divides the third side into segments, the difference between which is 8 cm. Find the perimeter of the triangle.

Let’s designate the rectangle with letters ABCD. AB = 20 cm, AD = 30 cm, AE is the bisector of angle A. It is necessary to find the perimeter of the resulting triangle ABE.

Since the angle A of the rectangle ABCB = 90 °, the bisector AE divides it in half:

BAE = EAD = 90/2;

BAE = EAD = 45 °;

The angles in a triangle add up to 180 °. Based on this, we find the angle BEA of triangle ABE:

BEA = 180 ° – B – BAE;

BEA = 180 ° – 90 ° – 45 °;

BEA = 45 °.

Since BEA = BAE = 45 ° – triangle ABE – isosceles;

AB = BE = 20 cm;

AE = 28.3 (by the Pythagorean theorem);

Perimeter of triangle ABE:

P = 20 + 20 + 28.3 = 68.3 cm.