l=2w+2 this is what the length is.
Perimeter (P) is P=2l+2w because there are two widths and two lengths in a rectangle.
Since we know that P=46 and l=2w+2, we can do this (substitute P and l):
46=2(2w+2)+2w
Then use the distributive property:
46=4w+4+2w
Solve for w:
46=6w+4
42=6w
w=7
So the width is 7.
To find the length, plug w=7 into l=2w+2
l=2(7)+2
l=14+2
l=16
So, the dimensions are 16 m x 7 m.