Answer:
The exact perimeter is [tex]18\sqrt{2}[/tex] meters.
This is approximately 25.5 meters (nearest tenth).
The area of the rectangle is 36 square meters.
Step-by-step explanation:
Area of a rectangle = width × length
Perimeter of a rectangle = (2 × width) + (2 × length)
Given:
Perimeter
[tex]\textsf{Perimeter}=2 \sqrt{18} +2\sqrt{72}[/tex]
[tex]=2 \sqrt{9 \cdot 2} +2\sqrt{36 \cdot 2}[/tex]
[tex]=2 \sqrt{9} \sqrt{2}+2\sqrt{36}\sqrt{2}[/tex]
[tex]=2 \cdot 3 \sqrt{2}+2\cdot 6\sqrt{2}[/tex]
[tex]=6 \sqrt{2}+12\sqrt{2}[/tex]
[tex]=18\sqrt{2} \textsf{ m}[/tex]
The exact perimeter is [tex]18\sqrt{2}[/tex] meters.
This is approximately 25.5 meters (nearest tenth).
Area
[tex]\textsf{Area}=\sqrt{18} \times \sqrt{72}[/tex]
[tex]=\sqrt{9 \cdot 2} \times \sqrt{36 \cdot 2}[/tex]
[tex]=3\sqrt{2} \times 6\sqrt{ 2}[/tex]
[tex]=18\sqrt{2}\sqrt{ 2}[/tex]
[tex]=18 \cdot 2[/tex]
[tex]=36 \textsf{ m}^2[/tex]
The area of the rectangle is 36 square meters.
