Question

Периметр равнобедренной трапеции равен 64, ее средняя линия равна боковой стороне. Найдите боковую сторону трапеции.

Answer 1

Пусть боковые стороны трапеции=средней линии=x, 

а два основания= z и y

Сосиавим систему:

(z+y)/2=x (cв-во средней линии)

z+y+x+x=64(периметр)

 

(z+y)/2=x

z+y=64-2x

 

подставляем:

(64-2x)/2=x

64-2x=2x

4x=64

x=16

Ответ:16

Answer 2

Calculating the Side Length of an Isosceles Trapezoid

To find the length of the side of the isosceles trapezoid, we can use the following information: - The perimeter of the trapezoid is 64. - The average of the bases is equal to one of the legs.

Let's denote the length of the side of the trapezoid as x.

The perimeter of a trapezoid can be calculated using the formula: Perimeter = sum of all sides

For an isosceles trapezoid, the formula for the perimeter can be expressed as: Perimeter = a + b1 + a + b2, where a is the length of the legs and b1 and b2 are the lengths of the bases.

Given that the perimeter is 64 and the average of the bases is equal to one of the legs, we can set up the equation: 2a + (b1 + b2)/2 = a + x

Solving for x will give us the length of the side of the trapezoid.

Let's proceed with the calculation.