Question

331. Середня лінія трапеції дорівнює 16 см. Знайдіть основи трапеції, якщо: 1) одна з них на 2 см менша від другої; 2) одна з них утричі більша за другу; 3) їх відношення дорівнює 3:5. решите пожалуста​

Answer 1

Ответ: 1) Основания = 15 и 17 см.

2) Основания = 8 и 24 см.

3) Основания = 12 и 20 см.

Объяснение:   1) Пусть одно основание = Х тогда другое основание = Х+2. Средняя линия = (Х +Х+2)/2 = (Х+1)  = 16.    Х = 16-1 = 15 см.  Второе основание = 15 + 2 = 17 см.

2) Одно основание = Х другое = 3Х. Тогда средняя линия  (Х + 3Х)/2 = 16 см. 4Х/2 = 16 см   2Х = 16 см   Х = 16/2 = 8 см. Второе основание = 8*3 =24 см.

3)  Средняя линия в частях = (3+5)/2 = 4 части. Но эти 4 части= 16 см, значит 1 часть = 16/4 = 4 см.  Тогда одно основание = 3*4 = 12 см, другое основание = 5*4 = 20 см.

Answer 2

Ответ:Средняя линия трапеции равна полусумме оснований

Номер1

(16•2-2):2=15 см

Меньшее основание трапеции 15 см

БОльшее основание 15+2=17 см

Номер 2

16•2:4=8 см

Меньшее основание 8 см

БОльшее основание

8•3=24 см

Номер 3

3+5=8 частей

Одна часть равна

32:8=4 см

Меньшее основание

4•3=12 см

БОльшее 4•5=20 см

Можно решить через Х

Меньшее основание ЗХ

БОльшее 5Х

3Х+5Х=32

8Х=32

Х=32:8

Х=4

Меньшее основание 4•3=12 см

БОльшее основание 4•5=20 см

Объяснение:

Answer 3

Problem Analysis

We are given that the average length of the median of a trapezoid is 16 cm. We need to find the lengths of the bases of the trapezoid in three different scenarios: 1. One base is 2 cm shorter than the other. 2. One base is three times larger than the other. 3. The ratio of the bases is 3:5.

Solution

Let's solve each scenario step by step:

Scenario 1: One base is 2 cm shorter than the other Let's assume the length of one base is x cm. According to the problem, the other base is 2 cm shorter, so its length would be (x - 2) cm. The average length of the median is given as 16 cm. Since the median is the average of the two bases, we can set up the following equation:

(x + (x - 2)) / 2 = 16

Simplifying the equation: (2x - 2) / 2 = 16 2x - 2 = 32 2x = 34 x = 17

Therefore, one base is 17 cm and the other base is (17 - 2) = 15 cm.

Scenario 2: One base is three times larger than the other Let's assume the length of one base is x cm. According to the problem, the other base is three times larger, so its length would be 3x cm. Again, the average length of the median is given as 16 cm. Setting up the equation:

(x + 3x) / 2 = 16

Simplifying the equation: 4x / 2 = 16 2x = 16 x = 8

Therefore, one base is 8 cm and the other base is 3 * 8 = 24 cm.

Scenario 3: The ratio of the bases is 3:5 Let's assume the length of one base is 3x cm and the length of the other base is 5x cm. The average length of the median is given as 16 cm. Setting up the equation:

((3x) + (5x)) / 2 = 16

Simplifying the equation: 8x / 2 = 16 4x = 16 x = 4

Therefore, one base is 3 * 4 = 12 cm and the other base is 5 * 4 = 20 cm.

Summary

Based on the given information, we have found the lengths of the bases of the trapezoid in three different scenarios: 1. One base is 17 cm and the other base is 15 cm. 2. One base is 8 cm and the other base is 24 cm. 3. One base is 12 cm and the other base is 20 cm.