Question

question 5/9
a 4 b
3
c
e d
the figure above, abcde represents a sign whose outside edge is going to be painted. if abde is a rectangle and angles ∠bcd, ∠cdb, and ∠dbc are all equal in measure, what is the length in feet of the perimeter of the entire sign?

Explanation:

Step1: Determine the type of triangle \(BCD\)

Since \(\angle BCD=\angle CDB = \angle DBC\), \(\triangle BCD\) is an equilateral triangle. So \(BC = CD=BD\). Given \(BC = 3\), then \(BD=3\).

Step2: Use the property of rectangle

In rectangle \(ABDE\), \(AB = ED = 4\) and \(AE=BD = 3\).

Step3: Calculate the perimeter

The perimeter \(P=AB + BC+CD + DE+EA\). Substitute the values: \(P = 4+3 + 3+4+3\).

Answer:

\(17\)