Answer: Length= 167 meters, Width= 40 meters
Step-by-step explanation:
We know that perimeter is the lengths of all sides of the rectangle added together. Therefore, the formula for perimeter is [tex]P=2l+2w[/tex]. We can use system of equations to find length and width.
[tex]P=2l+2w[/tex]
[tex]l=7+4w[/tex]
The second equation comes from the fact that the length is 7 meters more than 4 times the width.
Since we know the equation of [tex]l[/tex], we can use substitution to find [tex]l[/tex] and [tex]w[/tex].
[tex]P=2(7+4w)+2w[/tex]
[tex]P=14+8w+2w[/tex]
[tex]P=14+10w[/tex]
The problem gives us the perimeter to we can plug that into P.
[tex]414=14+10w[/tex]
[tex]400=10w[/tex]
[tex]w=40[/tex]
Now that we know the width, we can plug it into the equation to find length.
[tex]l=7+4(40)[/tex]
[tex]l=7+160[/tex][tex]l=167[/tex]
