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.

Explanation:

Step1: Identify similar triangles

The stairs form two similar right triangles, where the smaller triangle has a hypotenuse of 6 ft and base of 4 ft, and the larger triangle has a hypotenuse of 12 ft and unknown base $x$.

Step2: Set up proportion

Since corresponding sides of similar triangles are proportional:
$\frac{\text{Base of small triangle}}{\text{Hypotenuse of small triangle}} = \frac{\text{Base of large triangle}}{\text{Hypotenuse of large triangle}}$
$\frac{4}{6} = \frac{x}{12}$

Step3: Solve for $x$

Cross-multiply to isolate $x$:
$x = \frac{4 \times 12}{6}$
$x = 8$

Answer:

8