Question

Найди длины оснований равнобедренной трапеции, которая описана вокруг окружности, если боковая сторона этой трапеции равна 105 , а одно основание в 5 раз меньше другого.

Answer 1

Ответ:

35 ед. и 175 ед.

Объяснение:

Если в трапецию можно вписать окружность, то сумма боковых сторон равна сумме оснований.

105+105=210 (это сумма оснований или сумма боковых сторон)

Пусть меньшее основание х, тогда большее 5х.

х+5х=2104  6х=210   х=35

Меньшее основание 35, большее основание 35*5=175.

Answer 2

Problem Analysis

We are given a trapezoid that is circumscribed around a circle. We need to find the lengths of the bases of the trapezoid, given that one of the lateral sides is 105 units long and one base is 5 times smaller than the other base.

Solution

Let's assume that the shorter base of the trapezoid is x units long. According to the problem, the longer base will be 5x units long.

To find the lengths of the bases, we can use the properties of a trapezoid circumscribed around a circle. One of the properties states that the sum of the lengths of the bases of a trapezoid is equal to the sum of the lengths of the lateral sides.

In our case, the sum of the lengths of the bases is x + 5x = 6x, and the sum of the lengths of the lateral sides is 105 + 105 = 210.

Therefore, we can set up the following equation: 6x = 210

To find the value of x, we can solve this equation: x = 210 / 6 = 35

So, the shorter base of the trapezoid is 35 units long, and the longer base is 5 times longer, which is 5 * 35 = 175 units.

Answer

The lengths of the bases of the trapezoid are 35 units and 175 units, respectively.