Question

Середня лінія трапеції дорівнює 25 сантиментрів а її діагоналі в точці їх перетину діляться у відношенні 7 : 3 . Знайти основи трапеції

Answer 1

A,b-основания,(a+b)/2=25см
если диагонали делятся в отношении 7:3,то коэффициент подобия треугольников с основаниями a и b равен к=7/3
a/b=7/3 ⇒ a=7b/3
(7b/3+b)/2=25
10b/6=25
b=25;10/6=25*6/10
b=15
a=7*15/3
a=35

Answer 2

Finding the bases of a trapezoid

To find the bases of a trapezoid, we can use the given information about the midline and the diagonal. Let's denote the length of the midline as M and the length of the diagonal as D. We are also given that the diagonal divides the midline in a ratio of 7:3.

Let's solve this step by step:

1. We are given that the midline of the trapezoid is 25 centimeters. Let's denote this as M = 25 cm.

2. We are also given that the diagonal divides the midline in a ratio of 7:3. This means that the length of the segment on one side of the diagonal is 7/10 times the length of the midline, and the length of the segment on the other side is 3/10 times the length of the midline.

- Length of one segment = (7/10) * M - Length of the other segment = (3/10) * M

3. We are given that the diagonal intersects the midline at a point. Let's denote the length of the segment from the intersection point to one of the bases as x. Therefore, the length of the segment from the intersection point to the other base is (M - x).

4. According to the given information, the diagonal divides the midline in a ratio of 7:3. This means that the length of the segment from the intersection point to one of the bases is in a ratio of 7:3 with the length of the segment from the intersection point to the other base.

- Length of segment from intersection point to one base = (7/10) * M - Length of segment from intersection point to other base = (3/10) * M

5. We know that the length of the diagonal is equal to the sum of the lengths of the two segments from the intersection point to the bases.

- D = x + (M - x)

6. Substituting the values we have:

- D = x + (25 - x)

7. Simplifying the equation:

- D = 25

8. Therefore, the length of the diagonal is 25 centimeters.

Based on the given information, we can conclude that the length of the diagonal is 25 centimeters. However, we do not have enough information to determine the lengths of the bases of the trapezoid.