Question

a surveyor needs to measure the distance, ab, across the lake. beginning at e, he locates the midpoint, c, of ae and the midpoint, d, of be. he then measures cd. what is ab?

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment theorem states that the segment connecting the mid - points of two sides of a triangle is parallel to the third side and half its length. In \(\triangle EAB\), \(C\) is the mid - point of \(AE\) and \(D\) is the mid - point of \(BE\). So, \(CD\) is the mid - segment of \(\triangle EAB\).

Step2: Apply the mid - segment formula

According to the mid - segment formula \(CD=\frac{1}{2}AB\). Given \(CD = 47\) m. Then, \(AB = 2\times CD\).
Substitute \(CD = 47\) into the formula: \(AB=2\times47\).

Answer:

\(AB = 94\) m