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There is a stretched steel cable between the 3 columns. The height of the first column is 4 m, the height of the second is 3.5 m. The distance between the first two columns is 2.5 m, the distance between the second and third is 5 m. The heels of all three pillars stand in one line. What is the height of the third column?

Correct answer:

c =  2.5 m

Step-by-step explanation:

$$\begin{gathered} a=4\text{ m } \\ b=3.5\text{ m } \\ x=2.5\text{ m } \\ y=5\text{ m } \\ (a-b):x=(b-c):y \\ b-c={\displaystyle \frac{y}{x}}\cdot (a-b) \\ -c={\displaystyle \frac{y}{x}}\cdot (a-b)-b \\ c={\displaystyle \frac{y}{x}}\cdot (b-a)+b={\displaystyle \frac{5}{2.5}}\cdot (3.5-4)+3.5={\displaystyle \frac{5}{2}}={\displaystyle \frac{5}{2}}\text{ m}=2.5\text{ m} \end{gathered}$$

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