Answer:
The perimeter of one of the trapezoids is equal to 27.3 inches
Step-by-step explanation:
Given:
Perimeter of the large square tile = 48 inches
Perimeter of the smaller square = 16 inches
To Find :
The perimeter of one of the trapezoids
see the attached figure to better understand the problem
Solution:
we know that
The perimeter of a square is
P = [tex]4 \times sides[/tex]
step 1:Find the length side of the smaller square
[tex]16=4 \times side_{\small square}[/tex]
[tex]side_{\small square}= \frac{16}{4}[/tex]
[tex]side_{\small square}= 4 inches[/tex]
step 2 :Find the length side of the large square
[tex]48=4 \times side _{large square}[/tex]
[tex]side _{large square}=\frac{48}{4}[/tex]
[tex]side _{large square}=12 inches[/tex]
step 3: Find the height of one trapezoid
The height is equal to
[tex]h=\frac{(12-4)}{2}[/tex]=4 in
step 4: Find the hypotenuse of one isosceles right triangle
one trapezoid is equal to one square and two isosceles right triangles.
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]
P = 16 +8(1.414)
P= 16 + 11.28
P= 27.28
P =27.3
