Answer:
16cm
Step-by-step explanation:
Given
[tex]Area = 21cm^2[/tex]
[tex]Perimeter = 20cm[/tex]
[tex]n=4[/tex] --- rectangles
Required
The perimeter of square in the middle
The area of a rectangle is:
[tex]Area = L * W[/tex]
So, we have:
[tex]L * W =21[/tex]
The perimeter is:
[tex]P = 2*(L + W)[/tex]
So, we have:
[tex]2*(L + W) = 20[/tex]
Divide by 2
[tex]L + W = 10[/tex]
Make L the subject
[tex]L = 10 - W[/tex]
Substitute [tex]L = 10 - W[/tex] in [tex]L * W =21[/tex]
[tex](10 - W) * W = 21[/tex]
Open bracket
[tex]10W - W^2 = 21[/tex]
Rewrite as:
[tex]W^2 -10W +21 = 0[/tex]
Expand
[tex]W^2 -3W - 7W + 21 = 0[/tex]
Factorize
[tex]W(W - 3) - 7(W - 3) = 0[/tex]
Factor out W - 3
[tex](W - 7)(W - 3) = 0[/tex]
Solve for 7
[tex]W = 7\ W = 3[/tex]
We have:
[tex]L = 10 - W[/tex]
This means that:
[tex]W = 7\ W = 3[/tex]
[tex]L = 3,\ L = 7[/tex]
The length (l) of the square is:
[tex]l = |W - L|[/tex] ---- the difference between the dimension of the rectangle
[tex]l = |7 - 3|[/tex]
[tex]l = |4|[/tex]
[tex]l = 4[/tex]
The perimeter is:
[tex]P = 4l[/tex]
[tex]P = 4*4[/tex]
[tex]P =16[/tex]
