Let's denote the width of the rectangular plot as "W" meters. According to the information provided, the length is 6 meters longer than the width, so the length can be represented as "W + 6" meters.
The area of a rectangle is given by the formula: Area = Length × Width.
In this case, the area is 16 square meters, so we can write the equation:
Area = (W + 6) × W
Now, we can solve for the width (W):
16 = (W + 6) × W
Expand the equation:
16 = W^2 + 6W
Now, rearrange the equation to form a quadratic equation:
W^2 + 6W - 16 = 0
To solve this quadratic equation, you can use the quadratic formula:
W = (-B ± √(B^2 - 4AC)) / (2A)
In this case, A = 1, B = 6, and C = -16. Plug these values into the formula:
W = (-6 ± √(6^2 - 4 * 1 * (-16))) / (2 * 1)
W = (-6 ± √(36 + 64)) / 2
W = (-6 ± √100) / 2
W = (-6 ± 10) / 2
Now, calculate both possible values for W:
1. W = (-6 + 10) / 2 = 4 / 2 = 2 meters
2. W = (-6 - 10) / 2 = -16 / 2 = -8 meters
Since the width cannot be negative, we take the positive value.
So, the width of the plot is 2 meters, and the length is 2 + 6 = 8 meters.
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LJacuzar
thx we got the same answer:D just asked for double checking
Let's assume the width of Seth's rectangular plot is "x" meters.
According to the given information, the length of the plot is 6 meters longer than its width. Therefore, the length would be (x + 6) meters.
The area of a rectangle is calculated by multiplying its length and width. In this case, the area is given as 16 square meters.
So, we can set up the equation:
Length × Width = Area
(x + 6) × x = 16
Expanding the equation:
x^2 + 6x = 16
Rearranging the equation to a quadratic form:
x^2 + 6x - 16 = 0
Now, we can solve this equation by factoring, completing the square, or using the quadratic formula. Let's solve it by factoring:
(x + 8)(x - 2) = 0
Setting each factor equal to zero:
x + 8 = 0 or x - 2 = 0
Solving for x:
x = -8 or x = 2
Since the width cannot be negative, we can disregard x = -8. Thus, the width of the plot is 2 meters.
To find the length, we substitute the value of x into the expression (x + 6):
Length = x + 6 = 2 + 6 = 8 meters.
Therefore, the length of the plot is 8 meters, and the width is 2 meters.
Step-by-step explanation:
Certainly! Let's break down the problem step by step:
1. Let's assume the width of Seth's rectangular plot is "x" meters.
2. According to the given information, the length of the plot is 6 meters longer than its width. So, the length would be (x + 6) meters.
3. The area of a rectangle is calculated by multiplying its length and width. In this case, the area is given as 16 square meters. So we can set up the equation: Length × Width = Area, which becomes (x + 6) × x = 16.
4. We now have a quadratic equation: x^2 + 6x = 16.
5. To solve this equation, we rearrange it to the quadratic form: x^2 + 6x - 16 = 0.
6. Next, we need to factor the quadratic equation: (x + 8)(x - 2) = 0.
7. Setting each factor equal to zero, we have x + 8 = 0 or x - 2 = 0.
8. Solving for x, we find x = -8 or x = 2.
9. Since the width cannot be negative, we ignore x = -8.
10. Therefore, the width of the plot is 2 meters.
11. To find the length, we substitute the value of x into the expression (x + 6): Length = x + 6 = 2 + 6 = 8 meters.
12. Hence, the length of the plot is 8 meters, and the width is 2 meters.
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Verified answer
Answer:
Let's denote the width of the rectangular plot as "W" meters. According to the information provided, the length is 6 meters longer than the width, so the length can be represented as "W + 6" meters.
The area of a rectangle is given by the formula: Area = Length × Width.
In this case, the area is 16 square meters, so we can write the equation:
Area = (W + 6) × W
Now, we can solve for the width (W):
16 = (W + 6) × W
Expand the equation:
16 = W^2 + 6W
Now, rearrange the equation to form a quadratic equation:
W^2 + 6W - 16 = 0
To solve this quadratic equation, you can use the quadratic formula:
W = (-B ± √(B^2 - 4AC)) / (2A)
In this case, A = 1, B = 6, and C = -16. Plug these values into the formula:
W = (-6 ± √(6^2 - 4 * 1 * (-16))) / (2 * 1)
W = (-6 ± √(36 + 64)) / 2
W = (-6 ± √100) / 2
W = (-6 ± 10) / 2
Now, calculate both possible values for W:
1. W = (-6 + 10) / 2 = 4 / 2 = 2 meters
2. W = (-6 - 10) / 2 = -16 / 2 = -8 meters
Since the width cannot be negative, we take the positive value.
So, the width of the plot is 2 meters, and the length is 2 + 6 = 8 meters.
Answer:
Let's assume the width of Seth's rectangular plot is "x" meters.
According to the given information, the length of the plot is 6 meters longer than its width. Therefore, the length would be (x + 6) meters.
The area of a rectangle is calculated by multiplying its length and width. In this case, the area is given as 16 square meters.
So, we can set up the equation:
Length × Width = Area
(x + 6) × x = 16
Expanding the equation:
x^2 + 6x = 16
Rearranging the equation to a quadratic form:
x^2 + 6x - 16 = 0
Now, we can solve this equation by factoring, completing the square, or using the quadratic formula. Let's solve it by factoring:
(x + 8)(x - 2) = 0
Setting each factor equal to zero:
x + 8 = 0 or x - 2 = 0
Solving for x:
x = -8 or x = 2
Since the width cannot be negative, we can disregard x = -8. Thus, the width of the plot is 2 meters.
To find the length, we substitute the value of x into the expression (x + 6):
Length = x + 6 = 2 + 6 = 8 meters.
Therefore, the length of the plot is 8 meters, and the width is 2 meters.
Step-by-step explanation:
Certainly! Let's break down the problem step by step:
1. Let's assume the width of Seth's rectangular plot is "x" meters.
2. According to the given information, the length of the plot is 6 meters longer than its width. So, the length would be (x + 6) meters.
3. The area of a rectangle is calculated by multiplying its length and width. In this case, the area is given as 16 square meters. So we can set up the equation: Length × Width = Area, which becomes (x + 6) × x = 16.
4. We now have a quadratic equation: x^2 + 6x = 16.
5. To solve this equation, we rearrange it to the quadratic form: x^2 + 6x - 16 = 0.
6. Next, we need to factor the quadratic equation: (x + 8)(x - 2) = 0.
7. Setting each factor equal to zero, we have x + 8 = 0 or x - 2 = 0.
8. Solving for x, we find x = -8 or x = 2.
9. Since the width cannot be negative, we ignore x = -8.
10. Therefore, the width of the plot is 2 meters.
11. To find the length, we substitute the value of x into the expression (x + 6): Length = x + 6 = 2 + 6 = 8 meters.
12. Hence, the length of the plot is 8 meters, and the width is 2 meters.