Answer:
length = 8m and width = 6m
Explanation:
We are told that 28 Plants that are placed 1 m apart. This means that total perimeter of rectangular space = 28
Thus;
2L + 2W = 28
Divide both sides by 2 to get;
L + W = 14 - - - (eq 1)
Where;
L is length
W is width
Furthermore, we are told that he needs an inner rectangular space in the center for plants that must be 1 m From the border of the bed and that require 24 square meter for planting.
This means that;
(L - 2) × (W - 2) = 24
(L - 2)(W - 2) = 24
Divide both sides by (W - 2) to get;
L - 2 = 24/(W - 2)
From eq(1),we can say that;
L = 14 - W
Thus;
14 - W - 2 = 24/(W - 2)
(12 - W) = 24/(W - 2)
Multiply both sides by (W - 2) to get;
(12 - W)(W - 2) = 24
12W - W² + 2W - 24 = 24
W² - 14W + 48 = 0
From quadratic formula, we have;
[-(-14) ± √(-14)² - 4(1 × 48)]/(2 × 1)
This gives;
W = 8 or 6
From earlier, we saw that L = 14 - W
Thus, L = 14 - 6 = 8 or L = 14 - 8 = 6
Since values of W and L are similar, we will choose the higher value to be the length and the smaller value to be the width.
Thus, length = 8m and width = 6m