We can translate these sentences into equations:
"The perimeter of a rectangle is 62 m"
[tex]\sf P=2l+2w[/tex]
[tex]\sf 62=2l+2w[/tex]
"The length is four more than two times the width."
[tex]\sf l=2w+4[/tex]
Now we can plug in what 'l' equals in the 2nd equation into the first equation:
[tex]\sf 62=2l+2w[/tex]
[tex]\sf 62=2(2w+4)+2w[/tex]
Distribute:
[tex]\sf 62=4w+8+2w[/tex]
Combine like terms:
[tex]\sf 62=6w+8[/tex]
Subtract 8 to both sides:
[tex]\sf 54=6w[/tex]
Divide 6 to both sides:
[tex]\sf w=9[/tex]
So this is our width, we can plug this into any of the two equations to find the length:
[tex]\sf l=2w+4[/tex]
[tex]\sf l=2(9)+4[/tex]
Multiply:
[tex]\sf l=18+4[/tex]
Add:
[tex]\boxed{\sf l=22~m}[/tex]
