Answer:
[tex]perimeter=90[/tex]
Step-by-step explanation:
We know that the length is four times the width, so:
[tex]l=4w[/tex]
We also know the area, which is 324 m². The formula for area:
[tex]A=l*w[/tex]
Insert the known values:
[tex]324=(4w)*w[/tex]
Solve for w. Simplify by removing parentheses:
[tex]324=4w*w\\324=4w^2[/tex]
Divide 4 from both sides to isolate the variable:
[tex]\frac{324}{4}=\frac{4w^2}{4} \\\\81=w^2[/tex]
Find the square root of both sides:
[tex]\sqrt{81} =\sqrt{w^2} \\\\w=9[/tex]
The width is 9 m.
We know the width. Now find the length by using the area formula and inserting known values:
[tex]324=l*9[/tex]
Solve for l. Divide both sides by 9:
[tex]\frac{324}{9}=\frac{l*9}{9}\\\\ l=36[/tex]
The length of the rectangle is 36. (You can check: 4 times 9 is 36)
Now find the perimeter:
[tex]P=2l+2w[/tex]
Insert values:
[tex]P=2(36)+2(9)\\\\P=72+18\\\\P=90[/tex]
The perimeter is 90 m.
