In rectangle ABCD, the bisector of angle C divides side AB into segments of 8 cm and 20 cm. Calculate the perimeter ABCD.

univerkov | September 4, 2021 | education

1. Let’s designate by point К the place of intersection of the bisector with the side AB.

2. The length of the side AB of the rectangle: AK + ВK = 8 + 20 = 28 cm.

3. The bisector divides the angle at the vertex С in half, therefore the angle ВСК = 90 °: 2 = 45 °.

5. Angle КСD = 180 ° – 90 ° – 45 ° = 45 °.

6. The angles at the base of the CК of the ВCК triangle are equal. Therefore, this triangle is isosceles. This means that СВ = СK = 8 cm.

7. The perimeter of the rectangle is:

2AB + 2BC = 2 x 28 + 2 x 8 = 56 + 16 = 72 cm.

Answer: The perimeter of the rectangle is 72 cm.

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