Answer:
[tex]P = 30.5[/tex]
Step-by-step explanation:
Given
Similar Shapes: ABCD and EFGH
Required
Determine the perimeter of EFGH
First, we need to determine the complete sides of EFGH
Compare Similar Sides:
AB = 12 and EF =6
By comparison:
[tex]12 = 6 * 2[/tex]
i.e.
[tex]AB = EF * 2[/tex]
So, side FG will be solved using:
[tex]BC = FG * 2[/tex]
[tex]12 = FG * 2[/tex]
Divide both sides by 2
[tex]FG = 6[/tex]
Side GH will also be solved using:
[tex]CD = GH * 2[/tex]
[tex]12 = GH * 2[/tex]
Divide both sides by 2
[tex]GH = 6[/tex]
So, we have:
[tex]GH = 6[/tex] [tex]FG = 6[/tex] [tex]EF = 6[/tex] [tex]EH = 12.5[/tex]
The perimeter, P is then calculated as:
[tex]P = GH + EF + FG + EH[/tex]
[tex]P = 6 + 6 + 6 + 12.5[/tex]
[tex]P = 30.5[/tex]
