Answer: AE = 120.83 m DE= 148.66 m
The perimeter of the pentagon is 699.49
Sketch attached.
Step-by-step explanation: First we have to imagine the shape of the pentagon. In order to satisfy the requirement "that E is 50 m from the side AB and 30 m from the side BC," this must be a concave pentagon.
To determine the lengths of sides AE and DE, subtract the given distances of E from the lines, and use those values in the Pythagorean Theorem.
AE: [tex]110^{2}+50^{2}=14600[/tex] [tex]\sqrt{14600}=120.8304597[/tex]
DE: [tex]100^{2}+110^{2}=22100[/tex] [tex]\sqrt{22100}=148.6606875[/tex]
Add those lengths and the remaining sides of the "rectangle shown below" to calculate the perimeter.
280+150+120.83+148.66= 699.49
