Answer:
Part 1) [tex]P=(4x+4)\ units[/tex]
Part 2)
a) [tex]P=32\ units[/tex]
b) [tex]P=26\ units[/tex]
c) [tex]P=13\frac{1}{3}\ units[/tex]
Step-by-step explanation:
The complete question in the attached figure
Part 1) Write an expression for the perimeter of the shape
we know that
The figure is composed by a larger square, a rectangle and a smaller square
1) The area of the larger square is given
[tex]A=x^2\ units^2[/tex]
so
The length and the width of the larger square is x units
2) The area of the rectangle is given
[tex]A=x\ units^2[/tex]
so
The length of the rectangle is x units and the width is 1 unit
3) The length and the width of the smaller square is x units
see the attached figure N 2 to better understand the problem
Find out the perimeter
The perimeter is the sum of all the sides.
so
[tex]P=(x+x+x+x+1+1+1+1)[/tex]
[tex]P=(4x+4)\ units[/tex]
Part 2) Find the perimeter for each of the given values of x.
a) For x=7 units
Substitute the value of x in the expression of the perimeter
[tex]P=(4(7)+4)=32\ units[/tex]
b) For x=5.5 units
Substitute the value of x in the expression of the perimeter
[tex]P=(4(5.5)+4)=26\ units[/tex]
b) For x=7/3 units
Substitute the value of x in the expression of the perimeter
[tex]P=(4(\frac{7}{3})+4)=\frac{40}{3}=13\frac{1}{3}\ units[/tex]
