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There is a stretched steel cable between the three columns. The height of the first column is 4 m, and the height of the second is 3.5 m. The distance between the first two columns is 2.5 m, and 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?

Final Answer:

c =  2.5 m

Step-by-step explanation:

$$\begin{gathered} a=4\text{m} \\ b=3.5\text{m} \\ x=2.5\text{m} \\ y=5\text{m} \\ (a-b):x=(b-c):y \\ (a-b)/x=(b-c)/y \\ (4-3.5)/2.5=(3.5-c)/5 \\ c=2.5=2.5\text{m} \\ c=\frac{2.5}{1}=2.5 \\ c=\frac{5}{2}=2.5 \\ \text{ Verifying Solution: } \\ {k}_1=(a-b)/x=(4-3.5)/2.5=\frac{1}{5}=0.2 \\ {k}_2=(b-c)/y=(3.5-2.5)/5=\frac{1}{5}=0.2 \\ {k}_1=k_2 \end{gathered}$$

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