Question

the figure below shows a map of smiths compound for fish farming. the upper section is meant for rainbow trout while the lower section is for sturgeon. $\angle abd = \angle dbc$, while $\angle adb = \angle bdc$. if $\overline{db} = 75$ m and $\overline{bc} = 53$ m, what is the length of $\overline{ab}$?

Explanation:

Step1: Prove triangles congruent

In \(\triangle ABD\) and \(\triangle CBD\), \(\angle ABD=\angle DBC\) (given), \(DB = DB\) (common side), \(\angle ADB=\angle BDC\) (given). By the ASA (Angle - Side - Angle) congruence criterion, \(\triangle ABD\cong\triangle CBD\).

Step2: Use congruent triangles property

Since \(\triangle ABD\cong\triangle CBD\), then \(AB = BC\) (corresponding parts of congruent triangles are equal). Given \(BC = 53\) m.

Answer:

\(53\) m