The length and width are unknown.
Let the width = w.
The length is 1 more than 3 times the width.
3 times the width is 3 * w = 3w
1 more than 3 times the width is 3w + 1
We have length = 3w + 1, and width = w
The perimeter is the sum of the lengths of the 4 sides, two lengths and two widths.
P = L + L + W + W
P = 3w + 1 + 3w + 1 + w + w
Combining like terms, we get
P = 8w + 2
We are told the perimeter is 58 in., so we set our expression for the perimeter equal to 58
8w + 2 = 58
Now we solve for w, the width.
8w = 56
w = 7
The width is 7 in.
Now we solve for the length.
L = 3w + 1
L = 3(7) + 1 = 21 + 1 = 22
The length is 22 in.
The width is 7 in.