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: Use the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. In \(\triangle EAB\), \(C\) is the midpoint of \(AE\) and \(D\) is the midpoint of \(BE\). So, \(CD\) is the mid - segment of \(\triangle EAB\).
The formula is \(CD=\frac{1}{2}AB\).

Step2: Solve for \(AB\)

Given \(CD = 51\) m. From \(CD=\frac{1}{2}AB\), we can solve for \(AB\) by multiplying both sides of the equation by \(2\).
\(AB = 2\times CD\)
Substitute \(CD = 51\) into the equation: \(AB=2\times51\)

Answer:

\(AB = 102\) m