A landscape architect is designing a rectangular flowerbed to be border with 28 Plants that are placed 1 m apart. 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. What should the overall dimensions of the flowerbed be?

length = 8m and width = 6m

Step-by-step 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

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