The Perimeter of the given figure is:
B). 34 Perimeter
What is the perimeter?
Perimeter is described as the sum of all sides of a figure.
In this case,
[tex]Perimeter = FG + GH + HJ + JF[/tex]
Important Assumption:
Let the central intersection of line [tex]GH & FH be = O[/tex]
By Pythagoras Theorem,
[tex]Hypotenuse^2[/tex] [tex]= Base^2[/tex] [tex]+ Height^2[/tex]
In triangle OGF : [tex]OG^2 + OF^2 = GF^2[/tex]
[tex]FG = 4^2 + 9^2[/tex] [tex]= 81 + 16 = 97 FG =[/tex] [tex]\sqrt{97} = 9.8[/tex]
In triangle OGH : [tex]OG^2 + OH^2 = GH^2[/tex]
[tex]FJ = 4^2 + 6^2 = 16 + 36 = 52[/tex]
FJ [tex]=[/tex] [tex]\sqrt{52}[/tex] [tex]= 7.2[/tex]
Given that, [tex]FG = JF[/tex] & [tex]GH = HJ[/tex]
So,
[tex]JF = 9.8[/tex]
& [tex]HJ = 7.2[/tex]
Hence,
Perimeter [tex]= FG + GH + HJ + JF[/tex]
[tex]= 9.8 + 7.2 + 9.8 + 7.2[/tex]
[tex]= 34[/tex]
Thus, option B is the correct answer.
To learn more about "Perimeter" here:
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