Question

a flight of stairs is supported by two columns, as shown in the diag
the distance from the base of the stairs to the taller column is

Explanation:

Step1: Use the property of similar triangles

Since the two triangles formed by the columns and the stairs are similar, the ratios of their corresponding sides are equal. Let the unknown distance be \(x\) feet. The ratio of the lengths of the stair - parts is \(\frac{6}{12}\), and the ratio of the base - parts is \(\frac{4}{x}\).

Step2: Set up the proportion

We have the proportion \(\frac{6}{12}=\frac{4}{x}\). Cross - multiply to get \(6x = 12\times4\).

Step3: Solve for \(x\)

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Answer:

\(8\)