Question

type the correct answer in the box
the image shows a portion of a bridge supported by two vertical pillars built from the points b and c on the slope below
the length of the bridge between pillar b and pillar c is □□□□ feet

Explanation:

Step1: Use the property of similar triangles

Let the length between pillar \(B\) and pillar \(C\) be \(x\) feet.
Since the two - pillar - bridge - slope figures form similar triangles, we can use the proportion \(\frac{AB}{BC}=\frac{\text{segment on the top of }AB}{\text{segment on the top of }BC}\).
Here, \(AB = 50\) feet, \(BC=70\) feet, and the segment on the top of \(AB\) is \(40\) feet. Let the segment on the top of \(BC\) be \(x\) feet.
By the basic proportionality theorem (Thales' theorem) for similar triangles, \(\frac{AB}{AC}=\frac{\text{segment on the top of }AB}{\text{segment on the top of }AB + x}\), but a simpler way is \(\frac{AB}{BC}=\frac{40}{x}\) (because of the similarity of the two sub - triangles formed by the parallel pillars).
Since \(AB = 50\) and \(BC = 70\), we have \(\frac{50}{70}=\frac{40}{x}\).
Cross - multiply: \(50x=40\times70\).

Step2: Solve for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(56\)