Question

Точка пересечения диагоналей трапеции, средняя линия которой 56 см, отстоит от ее оснований на расстоянии 6 см и 8 см. Найдите основания трапеции.

Answer 1

(а+в)/2=56
а/в=6/8 из- за подобия треугольников, образованных точкой пересечения диагоналей.
а= 48
в= 64

Answer 2

Finding the Bases of the Trapezoid

To find the bases of the trapezoid, we can use the given information about the intersection point of its diagonals and the distance of its median line from the bases.

Given: - The median line of the trapezoid is 56 cm long. - The median line is at a distance of 6 cm and 8 cm from the bases.

Let's denote the bases of the trapezoid as \( a \) and \( b \).

Using the given information, we can set up the following equations: 1. The sum of the distances of the intersection point of the diagonals from the bases is equal to the length of the median line: \[ 6 + 8 = 56 \]

We can solve this equation to find the values of \( a \) and \( b \).

Calculating the Bases

Let's solve the equation to find the values of \( a \) and \( b \): \[ a + b = 56 \]

Given that the median line is 56 cm long and is equidistant from the bases