Question

Отрезок MH пересекает некоторую плоскость в точке K.Через концы отрезка проведены прямые HP И ME , перпендикулярные плоскости и пересекающие ее в точках P и E. Найдите PE,если HP=4 см, HK=5 см , ME=12 см.

Answer 1

Problem Analysis

We are given that segment MH intersects a certain plane at point K. Lines HP and ME are drawn through the ends of the segment, perpendicular to the plane, and intersect the plane at points P and E, respectively. We need to find the length of PE given that HP = 4 cm, HK = 5 cm, and ME = 12 cm.

Solution

To find the length of PE, we can use the concept of similar triangles. Since HP is perpendicular to the plane, triangle HKP is a right triangle. Similarly, triangle MEP is also a right triangle.

Let's denote the length of PE as x.

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

HP / HK = PE / ME

Substituting the given values, we have:

4 cm / 5 cm = x / 12 cm

To find the value of x, we can cross-multiply and solve for x:

4 cm * 12 cm = 5 cm * x

48 cm^2 = 5 cm * x

x = 48 cm^2 / 5 cm

x = 9.6 cm

Therefore, the length of PE is 9.6 cm.