A Garden 7m By12m Will Bi Expanded By Planting A Border Of F…

a garden 7m by12m will bi expanded by planting a border of flower. the border will be of the same width around the entire garden and has an area of 92m²​

[tex]\LARGE\tt✏ MATHEMATICS :[/tex]

To determine the width of the border, we can subtract the area of the original garden from the area of the expanded garden (including the border).

Given:

Length of the original garden = 7m

Width of the original garden = 12m

Area of the border = 92m²

Let’s assume the width of the border is ‘x’ meters.

The length of the expanded garden will be increased by twice the width of the border, as there will be a border on both sides. Similarly, the width of the expanded garden will be increased by twice the width of the border.

The length of the expanded garden, including the border, will then be (7 + 2x) meters, and the width will be (12 + 2x) meters.

The area of the expanded garden can be calculated as the product of the length and width:

(7 + 2x)(12 + 2x) = Area of the expanded garden

The area of the expanded garden is the sum of the area of the original garden and the area of the border:

(7 + 2x)(12 + 2x) = (7 x 12) + 92

Expanding the left side of the equation:

84 + 14x + 24x + 4x² = 84 + 92

Combining like terms:

4x² + 38x – 92 = 0

Now, we can solve this quadratic equation for ‘x’. Using factoring, the equation can be rewritten as:

(2x – 6)(2x + 23) = 0

Setting each factor equal to zero:

2x – 6 = 0 or 2x + 23 = 0

Solving for ‘x’:

2x = 6 or 2x = -23

x = 3 or x = -11.5

Since width cannot be negative, the width of the border is 3 meters.

Therefore, the border around the garden will be 3 meters wide.

CarryOnLearning

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