Question

ПОЖАЛУЙСТА ПОМОГИТЕ!!!!!!!!!найдите периметр прямоугольника abcd если биссектрисы его углов a и b делят сторону cd на три равные части

Answer 1

Прямоугольник АВСД, АК и ВН биссектрисы, СН=НК=КД=х, уголВНС=уголАВН как внутрениие разносторонниеп=уголНВС, треугольник ВСН равнобедренный, ВС=СН=АД=х
СД=СН+НК+КД=3х=АВ, периметр=3х+3х+х+х=8х

Answer 2

Calculating the Perimeter of Rectangle ABCD

To find the perimeter of rectangle ABCD, we can use the information provided about the bisectors of its angles and the division of side CD into three equal parts.

Given: - Bisectors of angles A and B divide side CD into three equal parts.

Solution:

The perimeter of a rectangle can be calculated using the formula: P = 2 * (a + b), where a and b are the lengths of the adjacent sides.

From the given information, we can derive the following: - The length of side CD is divided into three equal parts, so each part is CD/3.

Using the properties of a rectangle, we know that opposite sides are equal in length. Therefore, side CD is equal to side AB.

From the given information, we can also deduce that the bisectors of angles A and B divide side CD into three equal parts, which means that the bisectors intersect CD at points that are 2/3 and 1/3 of the length of CD.

Let's denote the length of side CD as x. Then, the lengths of the segments into which CD is divided are (2/3)x and (1/3)x.

Using this information, we can calculate the lengths of sides AB and BC, and then find the perimeter of the rectangle.

Calculation:

- Length of side AB = Length of side CD = x - Length of side BC = Length of side AD = (2/3)x

Now, we can calculate the perimeter using the formula: P = 2 * (AB + BC)

Substituting the values: P = 2 * (x + (2/3)x) P = 2 * (x + 2x/3) P = 2 * (3x/3 + 2x/3) P = 2 * (5x/3) P = (10/3)x

Therefore, the perimeter of rectangle ABCD is (10/3)x.

Conclusion:

The perimeter of rectangle ABCD, given the information about the bisectors of its angles and the division of side CD into three equal parts, is (10/3)x.