Answer:
The perimeter of one of the trapezoids is equal to [tex](16+8\sqrt{2})\ in[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The perimeter of a square is
[tex]P=4b[/tex]
where
b is the length side of the square
step 1
Find the length side of the smaller square
[tex]16=4b[/tex]
[tex]b=16/4=4\ in[/tex]
step 2
Find the length side of the large square
[tex]48=4b[/tex]
[tex]b=48/4=12\ in[/tex]
step 3
Find the height of one trapezoid
The height is equal to
[tex]h=(12-4)/2=4\ in[/tex]
step 4
Remember that in this problem, one trapezoid is equal to one square plus two isosceles right triangles.
Find the hypotenuse of one isosceles right triangle
Applying Pythagoras Theorem
[tex]c^{2}=4^{2} +4^{2} \\ \\c=4\sqrt{2}\ in[/tex]
step 5
Find the perimeter of one of the trapezoid
The perimeter is equal to
[tex]P=(4\sqrt{2} +4+4\sqrt{2}+12)\\ \\P=(16+8\sqrt{2})\ in[/tex]
