Question

Боковые стороны равнобедренной трапеции продолжены до пересечения в точке M .Основания трапеции равны 4см и 12см, боковая сторона равна 9,6 см. Найти расстояние от точки M до конца большего основания.

Answer 1

Ответ:

14,4 см.

Объяснение:

Answer 2

Finding the Distance from Point M to the End of the Larger Base of an Isosceles Trapezoid

To find the distance from point M to the end of the larger base of the isosceles trapezoid, we can use the properties of similar triangles. Let's break down the problem step by step:

1. Given information: - The trapezoid is isosceles, which means that the two non-parallel sides are equal in length. - The lengths of the bases are 4 cm and 12 cm. - One of the non-parallel sides (the lateral side) is 9.6 cm long. - The lateral side is extended until it intersects with the larger base at point M.

2. Identifying the triangles: - Let's consider two triangles: triangle ABC and triangle MDC. - Triangle ABC is the larger triangle formed by the larger base and the two non-parallel sides. - Triangle MDC is the smaller triangle formed by the lateral side, the extension of the lateral side, and the larger base.

3. Establishing similarity: - Since the trapezoid is isosceles, triangle ABC and triangle MDC are similar. - This means that the corresponding angles of the two triangles are equal, and the corresponding sides are proportional.

4. Setting up the proportion: - Let x be the distance from point M to the end of the larger base. - The length of the larger base is 12 cm. - The length of the lateral side is 9.6 cm. - Using the similarity of the triangles, we can set up the following proportion: ``` (x + 9.6) / 9.6 = 12 / 4 ```

5. Solving the proportion: - Cross-multiplying the proportion, we get: ``` 4(x + 9.6) = 9.6 * 12 ``` - Simplifying the equation: ``` 4x + 38.4 = 115.2 ``` - Subtracting 38.4 from both sides: ``` 4x = 76.8 ``` - Dividing both sides by 4: ``` x = 19.2 ```

6. Answer: - The distance from point M to the end of the larger base is 19.2 cm.

Please note that the search results provided by You.com did not contain specific information related to this problem. The solution was derived using the properties of similar triangles.