Answer:
Explanation:
To find the expression for the perimeter of the rectangular garden, we need to add up the lengths of all four sides. If the length of the garden is l and the width is w, then the perimeter P is given by:
P = 2l + 2w
We can write the length and width in terms of x, using the area expression 5x^2 - 18x + 9:
5x^2 - 18x + 9 = lw
Since the garden is rectangular, we can assume that the length and width are positive values, so we can find the length and width by finding the positive roots of the quadratic equation. We can factor the expression 5x^2 - 18x + 9 as:
5x^2 - 18x + 9 = (5x - 3)(x - 3)
Setting each factor equal to zero and solving for x, we get:
5x - 3 = 0 or x - 3 = 0
x = 3/5 or x = 3
Since the length and width must be positive values, we can take x = 3/5 as the width w, and x = 3 as the length l.
Therefore, the perimeter of the rectangular garden is:
P = 2l + 2w = 2(3) + 2(3/5) = 6 + 6/5 = 36/5
Simplifying the expression, we get:
P = 7.2x
Therefore, the simplified expression for the perimeter of the garden is 7.2x.