On a segment AB 45 cm long, point C is given. Find the length of segment CB if AC: BC = 7: 2.

From the condition we know that on the segment AB 45 cm long, point C is given. We also know that AC: BC = 7: 2. To find the lengths of the segments into which we divide the segment AB by point C, we will compose and solve a linear equation.

Let’s enter the coefficient of similarity k, then the lengths of the segments can be written as 7k and 2k.

Knowing the length of the entire segment, we get the equation:

7k + 2k = 45;

Here are similar ones:

k (7 + 2) = 45;

9k = 45;

k = 45: 9;

k = 5.

We found the value of the similarity coefficient and now we can write down the lengths of the segments:

7 * 5 = 35 cm and 2 * 5 = 10 cm.