The bisector of the corner of a rectangle bisects its larger side. The smaller side of the rectangle is 5 cm.

| December 21, 2020 | education

The bisector of the corner of a rectangle bisects its larger side. The smaller side of the rectangle is 5 cm. Find the sides of the rectangle.

Let’s designate the figure AВСD.
1. Consider a rectangle AВСD: VK is the bisector of angle B, AB = СD = 5 cm by the property of the sides of the parallelogram.
2. Consider a triangle ABK – rectangular, because AVSD is a rectangle, then the angle B = 90 °, and since ВK is a bisector and divides the angle B in half, then the AED angle = 45 °.
angle ВКА = 90 ° -45 ° = 45 °
Because the angles at the base are equal, then the triangle AВK is isosceles, which means AB = AK = 5cm.
3. Because ВK divides blood pressure in half, then AK = KD = 5cm.
means AD= AK + KD
BP = 5 + 5 = 10 cm
BC = AD = 10cm by the property of the sides of the parallelogram
Answer: 5, 10, 5, 10



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