The perimeter of a rectangle is the sum of visible lengths of the rectangle. The equivalent expressions are:
[tex]P = 2(4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)[/tex]
[tex]P = 2(3\sqrt 8) +2(4\sqrt{20} + 2\sqrt{24})[/tex]
[tex]P = 12\sqrt{2} + 16\sqrt{5} + 4\sqrt{6}[/tex]
Given that:
[tex]L = 4\sqrt{20} + 2\sqrt{24}[/tex] --- Length
[tex]W = 3\sqrt 8[/tex] --- Width
The perimeter (P) of the rectangle is:
[tex]P = 2 \times (L + W)[/tex]
So, we have:
[tex]P = 2 \times (4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)[/tex]
[tex]P = 2(4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)[/tex]
Rewrite as:
[tex]P = 2( 3\sqrt 8+4\sqrt{20} + 2\sqrt{24})[/tex]
Expand
[tex]P = 2(3\sqrt 8) +2(4\sqrt{20} + 2\sqrt{24})[/tex]
Further expand
[tex]P = 6\sqrt 8 +8\sqrt{20} + 2\sqrt{24}[/tex]
[tex]P = 6\sqrt{4\times 2} +8\sqrt{4\times 5} + 2\sqrt{4\times 6}[/tex]
Evaluate square roots
[tex]P = 6 \times 2\sqrt{2} +8\times 2\sqrt{5} + 2\times 2\sqrt{6}[/tex]
[tex]P = 12\sqrt{2} + 16\sqrt{5} + 4\sqrt{6}[/tex]
Hence, the equivalent expressions are:
[tex]P = 2(4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)[/tex]
[tex]P = 2(3\sqrt 8) +2(4\sqrt{20} + 2\sqrt{24})[/tex]
[tex]P = 12\sqrt{2} + 16\sqrt{5} + 4\sqrt{6}[/tex]
Read more about perimeters at:
https://brainly.com/question/6465134
