Question

В треугольнике АВС прямая MN параллельна АС, SABC : SBMN=49:25, MN=20 см. Найти АС. помогите плиз

Answer 1

Площади подобных треугольников относятся как квадраты подобия.  Отношение площадей равно 25/49. Значит, коэффициент подобия равен 5/7. Отсюда, сторона АС = 20: 5/7 = 28 см.

Answer 2

Finding the Length of AC in Triangle ABC

To find the length of AC in triangle ABC when the line MN is parallel to AC and SABC : SBMN = 49:25, with MN = 20 cm, we can use the concept of similar triangles and the property of parallel lines.

Using Proportionality in Similar Triangles

In a triangle, when a line is parallel to one side of the triangle, it creates similar triangles with the original triangle. In this case, triangle SBC and triangle SMN are similar because MN is parallel to AC. This means that the corresponding sides of these triangles are in proportion.

Applying the Proportionality Property

We can use the given ratio SABC : SBMN = 49:25 to find the ratio of the corresponding sides of the two similar triangles. Since the sides of similar triangles are in proportion, we can set up the following proportion:

SABC : SBMN = AC : MN

Substituting the given values, we get:

49:25 = AC : 20

Solving for AC

To find the length of AC, we can solve the proportion for AC:

AC = (49/25) * 20

Calculating the Length of AC

Calculating the value of AC:

AC = (49/25) * 20 = 39.2 cm

So, the length of AC in triangle ABC is 39.2 cm.