Answer:
Length = 2 feet
Width = 6 feet
Step-by-step explanation:
Let the length of a flower garden = l feet
And the width of the garden = w feet
Perimeter of the rectangular garden = 2(l + w)
16 = 2(l + w)
l + w = 8
l = 8 - w ---------(1)
Area of the rectangular garden = lw
12 = lw ---------(2)
By substituting the value of length in equation (2)
12 = (8 - w)w
12 = 8w - w²
w² - 8w + 12 = 0
w² - 6w - 2w + 12 = 0
w(w - 6) + 2(w - 6) = 0
(w + 2)(w - 6) = 0
w = -2, 6 feet
Since, width of the garden can't be negative.
Therefore, Width of the garden = 6 feet
From equation (1)
l = 2 feet
Therefore, length of the garden is 2 feet and width is 6 feet.
