The bisector of one of the corners of the rectangle divides one of its sides into two segments

The bisector of one of the corners of the rectangle divides one of its sides into two segments, the lengths of which are 12 and 8 cm. Calculate the lengths of the sides of the rectangle.

A rectangle is a rectangle in which all corners are straight.

Consider a triangle ΔАВК.

Since the bisector divides the angle in half, then:

∠АВК = 90 ° / 2 = 45 °.

Since the sum of all the angles of the triangle is 180 °, then:

∠AKВ = 180 ° – ∠ВAK – ∠AВK;

∠AKВ = 180 ° – 90 ° – 45 ° = 45 °.

This triangle is isosceles, since the angles at the base are equal.

Based on this:

AB = AK = 12 cm.

Since the bisector divides the BP side into 12 cm and 8 cm segments, then:

AD = AK + KD;

BP = 12 + 8 = 20 cm.

Answer: AB side is 12 cm, BP side is 20 cm.