Question

Дано: MN - средняя линия треугольника АВС. Перимеитр треугольника MBN=15 см, MB=4 см. NC=5 см. Найти АС.

Answer 1

Решение: 
Средняя линия делит стороны пополам,из этого следует BN=5см
MN=15-(4+5)=6
Следует по теореме о средней линии, средняя линия равна половине паралельной ей стороне АС=6+6=12см
Ответ: АС=12см


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Answer 2

Task: Find the length of AC in triangle ABC, given that MN is the median line, the perimeter of triangle MBN is 15 cm, MB = 4 cm, and NC = 5 cm.

To find the length of AC in triangle ABC, we can use the fact that MN is the median line. The median line in a triangle divides the opposite side into two equal segments. Therefore, we can conclude that MC = NC = 5 cm.

We are also given that the perimeter of triangle MBN is 15 cm. The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter of MBN is MB + BN + NM. Since MN is the median line, BN is equal to MB. Therefore, the perimeter of MBN can be expressed as 2MB + NM.

From the given information, we know that MB = 4 cm and NC = 5 cm. Let's substitute these values into the equation for the perimeter of MBN:

2MB + NM = 15 cm

2(4 cm) + NM = 15 cm

8 cm + NM = 15 cm

Now, let's solve for NM:

NM = 15 cm - 8 cm

NM = 7 cm

We have found that NM is equal to 7 cm. Since MN is the median line, we can conclude that AM = MC = 7 cm.

To find the length of AC, we need to add the lengths of AM and MC:

AC = AM + MC

AC = 7 cm + 5 cm

AC = 12 cm

Therefore, the length of AC in triangle ABC is 12 cm.

Answer:

The length of AC in triangle ABC is 12 cm.