Question

Перпендикулярно высоте ВD треугольника АВС проведина пересекает сторону АВ и ВС в точке М и Р.Найдите АВ и отношение рлощядей треугольников МРВ и АВС если известно Ю что МВ=7 ВР=9 РС=18

Answer 1

ВМ/ВР = АМ/СР (отношение) 

подставим известные нам данные в это отношение: 

7/9 = АМ/18 
АМ=7*18/9=14см
АВ=АМ+ВМ=14+7=21см
7/14 = 9/18= 1/2 (отношение площадей)

Ответ:  $\frac{1}{2}$

Answer 2

Perpendicular to the Height of Triangle ABC

To find the length of AB and the ratio of the areas of triangles MRV and ABC, we need to use the given information and apply some geometric principles.

Let's break down the problem step by step:

1. We are given that BD is perpendicular to the height of triangle ABC. This means that BD is an altitude of triangle ABC.

2. The altitude BD intersects sides AB and BC at points M and R, respectively.

3. We are also given that MV = 7, VR = 9, and RC = 18.

Now, let's proceed with finding the length of AB and the ratio of the areas of triangles MRV and ABC.

Finding the Length of AB

To find the length of AB, we can use the concept of similar triangles. Since BD is perpendicular to the height of triangle ABC, triangles ABD and BCD are similar to triangle ABC.

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

AB/BD = BC/CD

Since BD is an altitude, its length is equal to the height of triangle ABC. Let's denote the height of triangle ABC as h.

AB/h = BC/CD

We are given that MV = 7, VR = 9, and RC = 18. Therefore, CD = VR + RC = 9 + 18 = 27.

Substituting the values into the proportion, we have:

AB/h = BC/27

To find AB, we need to find BC. We can use the Pythagorean theorem to find BC.

BC^2 = BD^2 - CD^2

Since BD is an altitude, its length is equal to the height of triangle ABC, which is h.

BC^2 = h^2 - 27^2

Now, we need to find h. We can use the Pythagorean theorem again.

h^2 = MV^2 - BD^2

Substituting the given values, we have:

h^2 = 7^2 - BD^2

To find BD, we can use the Pythagorean theorem once more.

BD^2 = MV^2 - VR^2

Substituting the given values, we have:

BD^2 = 7^2 - 9^2

Now, we can substitute the values of BD^2 and MV^2 into the equation for h^2:

h^2 = 7^2 - (7^2 - 9^2)

Simplifying the equation, we have:

h^2 = 9^2

Taking the square root of both sides, we find:

h = 9

Now, we can substitute the value of h into the equation for BC^2:

BC^2 = 9^2 - 27^2

Simplifying the equation, we have:

BC^2 = -540

Since the length of a side cannot be negative, we can conclude that there is no real solution for BC. Therefore, it is not possible to determine the length of AB with the given information.

Ratio of the Areas of Triangles MRV and ABC

Since we were unable to determine the length of AB, we cannot calculate the ratio of the areas of triangles MRV and ABC.

In summary, based on the given information, we cannot determine the length of AB or the ratio of the areas of triangles MRV and ABC.