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A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?
Correct answer is '13'. Can you explain this answer?
Most Upvoted Answer
A landscaper is designing a rectangular garden. The length of the gard...
Given:
- The length of the garden is 5 feet longer than the width.
- The area of the garden is 104 square feet.
To find:
- The length of the garden.
Solution:
Let's assume the width of the garden as 'x' feet.
Area of a Rectangle:
The area of a rectangle is calculated by multiplying the length and width. In this case, the area is given as 104 square feet.
Area = Length * Width
We can substitute the given values into the equation:
104 = Length * x
Relationship between Length and Width:
According to the given information, the length of the garden is 5 feet longer than the width. Mathematically, we can express this relationship as:
Length = Width + 5
Substituting Length in terms of Width:
We can substitute the value of Length in terms of Width in the area equation:
104 = (Width + 5) * Width
Simplifying the Equation:
We can simplify the equation by multiplying the terms:
104 = Width^2 + 5Width
Arranging the Equation:
We can rearrange the equation in standard form:
Width^2 + 5Width - 104 = 0
Solving the Quadratic Equation:
To find the width of the garden, we need to solve the quadratic equation. We can either factorize the equation or use the quadratic formula.
Factoring the equation may not be straightforward, so we can use the quadratic formula:
Width = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 5, and c = -104.
Width = (-5 ± √(5^2 - 4*1*(-104))) / (2*1)
Width = (-5 ± √(25 + 416)) / 2
Width = (-5 ± √441) / 2
Width = (-5 ± 21) / 2
We have two possible values for Width: (-5 + 21)/2 = 16/2 = 8 and (-5 - 21)/2 = -26/2 = -13.
Since the width cannot be negative, we discard the negative value.
Calculating Length:
Now that we have the width, we can calculate the length using the relationship given:
Length = Width + 5
Length = 8 + 5
Length = 13
Therefore, the length of the garden is 13 feet.
- The length of the garden is 5 feet longer than the width.
- The area of the garden is 104 square feet.
To find:
- The length of the garden.
Solution:
Let's assume the width of the garden as 'x' feet.
Area of a Rectangle:
The area of a rectangle is calculated by multiplying the length and width. In this case, the area is given as 104 square feet.
Area = Length * Width
We can substitute the given values into the equation:
104 = Length * x
Relationship between Length and Width:
According to the given information, the length of the garden is 5 feet longer than the width. Mathematically, we can express this relationship as:
Length = Width + 5
Substituting Length in terms of Width:
We can substitute the value of Length in terms of Width in the area equation:
104 = (Width + 5) * Width
Simplifying the Equation:
We can simplify the equation by multiplying the terms:
104 = Width^2 + 5Width
Arranging the Equation:
We can rearrange the equation in standard form:
Width^2 + 5Width - 104 = 0
Solving the Quadratic Equation:
To find the width of the garden, we need to solve the quadratic equation. We can either factorize the equation or use the quadratic formula.
Factoring the equation may not be straightforward, so we can use the quadratic formula:
Width = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 5, and c = -104.
Width = (-5 ± √(5^2 - 4*1*(-104))) / (2*1)
Width = (-5 ± √(25 + 416)) / 2
Width = (-5 ± √441) / 2
Width = (-5 ± 21) / 2
We have two possible values for Width: (-5 + 21)/2 = 16/2 = 8 and (-5 - 21)/2 = -26/2 = -13.
Since the width cannot be negative, we discard the negative value.
Calculating Length:
Now that we have the width, we can calculate the length using the relationship given:
Length = Width + 5
Length = 8 + 5
Length = 13
Therefore, the length of the garden is 13 feet.
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Community Answer
A landscaper is designing a rectangular garden. The length of the gard...
Let w represent the width of the rectangular garden, in feet. Since the length of the garden will be 5 feet longer than the width of the garden, the length of the garden will be w + 5 feet. Thus the area of the garden will be w(w + 5). It is also given that the area of the garden will be 104 square feet. Therefore, w(w + 5) = 104, which is equivalent to w2 + 5w − 104 = 0. The quadratic formula can be used or the equation above can be factored to result in (w + 13)(w − 8) = 0. Therefore, w = 8 and w = −13. Because width cannot be negative, the width of the garden must be 8 feet. This means the length of the garden must be 8 + 5 = 13 feet.
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A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?Correct answer is '13'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?Correct answer is '13'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?Correct answer is '13'. Can you explain this answer?.
A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?Correct answer is '13'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?Correct answer is '13'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?Correct answer is '13'. Can you explain this answer?.
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