Question

Боковые стороны трапеции равны 4,5 см, а её периметр 69 см. Найти среднюю линию трапецию и основанию трапеции если известна что одно из них меньше другого в 2 раза.

Answer 1

Пусть меньшее основание х,тогда боььшее 2х. Составим уравнение:3х+9=69
3х=60
х=20
большее осн равно 2х то есть 20*2=40
средняя линия равна половине суммы осн ,то есть( 20+40)/2=30см

Answer 2

Problem Analysis

We are given that the lateral sides of a trapezoid are equal to 4.5 cm, and the perimeter of the trapezoid is 69 cm. We need to find the length of the median line and the length of the base of the trapezoid, given that one of them is smaller than the other by a factor of 2.

Solution

Let's denote the length of the median line as m and the length of the base as b.

We know that the perimeter of a trapezoid is the sum of all its sides. In this case, we have two equal lateral sides, so the perimeter can be expressed as:

69 cm = 2 * 4.5 cm + m + b

Simplifying the equation, we get:

69 cm = 9 cm + m + b

Now, we are given that one of the lengths is smaller than the other by a factor of 2. Let's assume that the length of the base, b, is the smaller length. Therefore, we can express the length of the median line as:

m = 2b

Substituting this into the previous equation, we have:

69 cm = 9 cm + 2b + b

Simplifying the equation further, we get:

69 cm = 9 cm + 3b

Subtracting 9 cm from both sides of the equation, we have:

60 cm = 3b

Dividing both sides of the equation by 3, we get:

20 cm = b

So, the length of the base of the trapezoid is 20 cm.

Now, we can substitute this value back into the equation for the length of the median line:

m = 2b = 2 * 20 cm = 40 cm

Therefore, the length of the median line is 40 cm.

Answer

The length of the base of the trapezoid is 20 cm, and the length of the median line is 40 cm.