Question

Ломаная состоит из трёх отрезков МК, КР и РN. Известно, что отрезок PN равен 5,7 см и он больше отрезка КР на 4,4 см и меньше отрезка МК 2,8 см. Найдите длину доманой.

Answer 1

Problem Analysis

We are given that a broken line consists of three segments: MK, KR, and RN. We are also given that the length of segment PN is 5.7 cm, which is 4.4 cm longer than segment KR and 2.8 cm shorter than segment MK. We need to find the length of the broken line.

Solution

Let's assume the length of segment KR is x cm.

According to the given information: - Segment PN is 4.4 cm longer than segment KR, so the length of PN is x + 4.4 cm. - Segment PN is 2.8 cm shorter than segment MK, so the length of MK is x + 4.4 cm + 2.8 cm = x + 7.2 cm.

The length of the broken line is the sum of the lengths of the three segments: MK, KR, and RN.

Therefore, the length of the broken line is: MK + KR + RN = (x + 7.2 cm) + x + (5.7 cm) = 2x + 12.9 cm.

To find the value of x, we can use the fact that segment PN is 5.7 cm long. We know that PN is equal to MK + KR, so we can write the equation:

MK + KR = PN x + 7.2 cm + x = 5.7 cm

Simplifying the equation: 2x + 7.2 cm = 5.7 cm 2x = 5.7 cm - 7.2 cm 2x = -1.5 cm x = -0.75 cm

Since the length of a segment cannot be negative, we can conclude that there is no valid solution for this problem.