Arectangle has a perimeter of 18 in its area is also 18 square in what are the length and width of the rectangle

Let the length be x and the width be y.

The perimeter is 18 in.
2 ( x + y ) = 18
x + y = 9
x = 9 - y (1)

The area is 18 in²
xy = 18
x = 18/y . (2)

Sub (1) into (2):
9 - y = 18/y

Multiply by y on both sides:
9y - y² = 18
y² - 9y + 18 = 0
(y - 3)(y - 6) = 0
y = 3 or y = 6

When y = 6
x = 9 - y = 9 - 6 = 3

Find the Length and Width:
Length = x = 6
Width =  y = 3

The length is 6 inches and the width is 3 inches.