Question

В трапеции АВСД боковые стороны АВ=13см СД= 15 см. Периметр равен 48 см. Найти среднию линию трапеции МН.

Answer 1

(48-13-15)/2=20/2=10 см

Answer 2

Task: Find the length of the median line MN of trapezoid ABCD.

To find the length of the median line MN of trapezoid ABCD, we can use the formula for the length of the median line in a trapezoid. The formula for the length of the median line MN in a trapezoid is:

Length of MN = (1/2) * (Sum of the lengths of the bases of the trapezoid)

Given: - Side AB = 13 cm - Side CD = 15 cm - Perimeter of the trapezoid = 48 cm

Calculation:

Using the given information, we can calculate the length of the median line MN.

Step 1: Calculate the length of the bases of the trapezoid. - Let's assume the length of side AB as a and the length of side CD as b. - We know that the perimeter of a trapezoid is the sum of all its sides. In this case, the perimeter is 48 cm. - So, we can write the equation as: a + b + AB + CD = 48 cm.

Step 2: Use the formula for the length of the median line MN. - The formula for the length of the median line MN in a trapezoid is: Length of MN = (1/2) * (a + b).

Solution:

Using the given information and the formula, we can calculate the length of the median line MN.

Step 1: Calculate the length of the bases of the trapezoid. - Let's assume the length of side AB as a and the length of side CD as b. - We know that the perimeter of a trapezoid is the sum of all its sides. In this case, the perimeter is 48 cm. - So, we can write the equation as: a + b + 13 + 15 = 48 cm. - Solving for a + b, we get: a + b = 48 - 13 - 15 = 20 cm.

Step 2: Use the formula for the length of the median line MN. - The formula for the length of the median line MN in a trapezoid is: Length of MN = (1/2) * (a + b). - Substituting the value of a + b, we get: Length of MN = (1/2) * 20 = 10 cm.

Answer:

The length of the median line MN of trapezoid ABCD is 10 cm.