Question

type the correct answer in the box. a flight of stairs is supported by two columns, as shown in the diagram. the distance from the base of the stairs to the taller column is feet. reset next

Explanation:

Step1: Use the property of similar triangles

Let the distance from the base of the stairs to the taller column be \(x\) feet.
Since the two triangles (formed by the columns and the stairs) are similar, we have the proportion \(\frac{6}{12}=\frac{4}{x}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(6x = 12\times4\).
Then \(6x=48\).
Divide both sides by 6: \(x=\frac{48}{6}\).

Answer:

\(8\)