Question

Боковая сторона равнобедренной трапеции равна 18 см,а средняя линия-16 см.Найдите периметр трапеции.

Answer 1

Средняя линия трапеции равна половине суммы оснований, таким образом сумма оснований трапеции равна двум средним линиям, таким образом, периметр трапеции будет равен: (18+16)·2= 68 (см).

Answer 2

Perimeter of a Trapezoid

To find the perimeter of a trapezoid, we need to know the lengths of all its sides. In this case, we are given that the length of the lateral side of the isosceles trapezoid is 18 cm, and the length of the median line (also known as the average of the bases) is 16 cm.

Let's denote the lengths of the bases of the trapezoid as a and b. The lateral side of the trapezoid is perpendicular to the bases and forms a right triangle with them. The median line divides the trapezoid into two congruent right triangles.

To find the lengths of the bases, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse (the lateral side) is equal to the sum of the squares of the other two sides (the bases). Therefore, we have:

a^2 + b^2 = 18^2

Since the median line is the average of the bases, we can write:

16 = (a + b) / 2

Solving these two equations simultaneously will give us the values of a and b.