# A surveyor made the measurements shown in the diagram below.What is the measure, in feet, of AB, the straight-line distance across the stream?

(D) 100

Explanation

You must recognize similar triangles in the diagram and set up the correct proportion, which could be expressed as: $$\frac{A C}{E C}=\frac{A B}{E D}$$
Letting AB be represented by x and substituting the other measures from the diagram, the proportion is then solved for the unknown measure.
$$\frac{A C}{E C}=\frac{A B}{E D}$$becomes $$\frac{{40}}{{10}} = \frac{x}{{25}}$$
Cross-multiplying: 10x = 1000
Dividing by 10: x = 100
The final answer is 100 feet.