Question

Через вершину В равнобедренного треугольника АВС (АВ = ВС) к плоскости треугольника проведен перпендикуляр BD длиной 5 см. Найдите расстояние от точки D до стороны АС, если АС = 8 см, АВ = 6 см.

Answer 1

решение во вложении
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Answer 2

Problem Analysis

We are given an isosceles triangle ABC, where AB = BC. A perpendicular BD of length 5 cm is drawn from the vertex B to the plane of the triangle. We need to find the distance from point D to the side AC, given that AC = 8 cm and AB = 6 cm.

Solution

To find the distance from point D to the side AC, we can use the property of similar triangles. Let's denote the distance from D to AC as x.

According to the property of similar triangles, we have the following ratio:

BD/DC = AB/AC

Substituting the given values, we get:

5/x = 6/8

Simplifying the equation, we have:

5/x = 3/4

Cross-multiplying, we get:

4 * 5 = 3 * x

20 = 3x

Dividing both sides by 3, we find:

x = 20/3

Therefore, the distance from point D to the side AC is 20/3 cm.

Answer

The distance from point D to the side AC is 20/3 cm.