1(!). The perimeter of a triangle is \(12 \mathrm{~cm}\), and the length of one of its sides is 5 cm. Find the relationship between the lengths of the other two sides and plot the graph of this relationship.
1. Solution. Let the length of the second side be \(x\) cm, and the third side be \(y\) cm. The length of each side is a positive number that is less than half the perimeter of the triangle. Therefore,

![](https://cdn.mathpix.com/cropped/2024_05_21_ffd37dfe6eab44561342g-75.jpg?height=680&width=685&top_left_y=251&top_left_x=340)

Fig. 29

![](https://cdn.mathpix.com/cropped/2024_05_21_ffd37dfe6eab44561342g-75.jpg?height=665&width=668&top_left_y=267&top_left_x=1048)

Fig. 30

\(0 < x < 6\), \(0 < y < 6\). Additionally, from the conditions of the problem, it follows that \(x + y = 7\), and therefore \(y = 7 - x\). The graph of the dependence is shown in Figure 29. The dependence between \(x\) and \(y\) can be written as: \(y = 7 - x\) and \(1 < x < 6\).