Answer: The perimeter is 96 m
Step-by-step explanation:
If we tag the length of the rectangle as [tex]l[/tex] and the width as [tex]w[/tex], and if in addition we are told [tex]l=5 w[/tex],the dimensions of the rectangle are as shown in the figure.
Now, the area of a rectangle is given by:
[tex]A=(l)(w)=320 m^{2}[/tex]
Since [tex]l=5 w[/tex]:
[tex]A=(5w)(w)=320 m^{2}[/tex]
Isolating [tex]w[/tex]:
[tex]5w^{2}=320 m^{2}[/tex]
[tex]w=\sqrt{\frac{320 m^{2}}{5}}[/tex]
[tex]w=8 m[/tex]
On the other hand, the perimeter of a triangle is given by the addition of each of its sides. Then, if the rectangle has two sides that measure [tex]w[/tex] and two sides that measure [tex]5 w[/tex], the perimeter is:
[tex]P=2(5)(w)+2w[/tex]
Substituting the value of [tex]w[/tex] in the last equation:
[tex]P=2(5)(8 m)+2(8 m)[/tex]
Finally the perimeter is:
[tex]P=96 m[/tex]
