Question

Боковые стороны равнобедренной трапеции продолжены до пересечения в точке М. Основания трапеции равны 2 см и 4,8 см, боковая сторона равна 4,2 см. Найти расстояние от точки М до конца большего основания.

Answer 1

Равнобедренная трапеция достраивается до равнобедренного треугольника...
искомое расстояние --это боковая сторона равнобедренного треугольника))
треугольники AMD и BMC будут подобны по двум углам))

Answer 2

Problem Analysis

We are given a trapezoid with equal legs, and the side lengths of the trapezoid are 2 cm and 4.8 cm. We need to find the distance from point M to the end of the longer base.

Solution

To find the distance from point M to the end of the longer base, we can use the concept of similar triangles. Let's denote the length of the longer base as B, the length of the shorter base as b, and the length of the side as a.

Since the trapezoid has equal legs, we can conclude that the triangles formed by the sides of the trapezoid and the line segment connecting point M to the end of the longer base are similar.

Using the concept of similar triangles, we can set up the following proportion:

(MB / a) = (B / b)

We know the values of a, b, and MB. We need to find the value of B.

Let's substitute the given values into the proportion and solve for B:

(MB / 4.2) = (B / 2)

Cross-multiplying the proportion, we get:

MB * 2 = 4.2 * B

Simplifying the equation, we have:

2 * MB = 4.2 * B

Dividing both sides of the equation by 2, we get:

MB = 2.1 * B

Now, we can substitute the value of MB into the equation:

2.1 * B = 4.2 * B

Dividing both sides of the equation by 4.2, we get:

B = 2.1

Therefore, the length of the longer base (B) is 2.1 cm.

Now, we can find the distance from point M to the end of the longer base by subtracting the length of the shorter base (b) from the length of the longer base (B):

Distance from M to the end of the longer base = B - b = 2.1 cm - 4.8 cm = -2.7 cm

Note: The negative value indicates that the end of the longer base is to the left of point M.

Answer

The distance from point M to the end of the longer base is -2.7 cm.