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

January 27, 2021 | education

| **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.

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