Final answer:
To determine the width of the strip that would double the area of the garden, we can set up an equation. The original area of the garden is 8m * 12m = 96m². Let's assume the width of the strip is x meters. Adding the strip will increase the length and width of the garden by 2x (1x on each side), so the dimensions of the enlarged garden will be (8+2x) meters by (12+2x) meters. The new area of the garden with the strip is (8+2x)(12+2x). According to the question, the new area should be double the original area. So we can write the equation: (8+2x)(12+2x) = 2(96). Using FOIL to expand, we can simplify the equation to 4x² + 40x - 96 = 0. Solving this quadratic equation gives us two possible values for x, 2 and -12. Since the width cannot be negative, we choose x = 2. Therefore, the width of the strip that will double the area of the garden is 2 meters.
Step-by-step explanation:
To determine the width of the strip that would double the area of the garden, we can set up an equation. The original area of the garden is 8m * 12m = 96m². Let's assume the width of the strip is x meters. Adding the strip will increase the length and width of the garden by 2x (1x on each side), so the dimensions of the enlarged garden will be (8+2x) meters by (12+2x) meters. The new area of the garden with the strip is (8+2x)(12+2x).
According to the question, the new area should be double the original area. So we can write the equation:
(8+2x)(12+2x) = 2(96)
Using FOIL to expand:
96 + 16x + 24x + 4x² = 192
Combine like terms:
4x² + 40x - 96 = 0
Now we can solve this quadratic equation for x. We can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Where a = 4, b = 40, and c = -96. Plugging in the values:
x = (-40 ± √(40^2 - 4*4*(-96)))/(2*4)
Simplifying the expression under the square root:
√(40^2 - 4*4*(-96)) = √(1600 + 1536) = √(3136) = 56
Now substituting back into the quadratic formula:
x = (-40 ± 56)/(8)
This gives two possible values for x:
x = (-40 + 56)/8 = 16/8 = 2
x = (-40 - 56)/8 = -96/8 = -12
Since the width cannot be a negative value, we choose x = 2. Therefore, the width of the strip that will double the area of the garden is 2 meters.