A Rectangular Parking Lot Has A Length That Is 7 Meters Greater Than The Width. The Area Of The Parking Lot Is 120 Square Meters. Find The Length And The Width.
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Introduction
In this article, we will delve into the world of mathematics and solve a problem involving a rectangular parking lot. The problem states that the length of the parking lot is 7 meters greater than the width, and the area of the parking lot is 120 square meters. Our goal is to find the length and the width of the parking lot.
Understanding the Problem
Let's break down the problem and understand what is being asked. We have a rectangular parking lot with a length that is 7 meters greater than the width. This means that if we let the width be x, then the length will be x + 7. The area of the parking lot is given as 120 square meters.
Formulating the Equation
To find the length and the width of the parking lot, we need to formulate an equation based on the given information. The area of a rectangle is given by the formula:
Area = Length × Width
In this case, the area is 120 square meters, and the length is x + 7. So, we can write the equation as:
120 = (x + 7) × x
Solving the Equation
Now that we have formulated the equation, let's solve it to find the value of x, which represents the width of the parking lot. To solve the equation, we can start by expanding the right-hand side:
120 = x^2 + 7x
Next, we can rearrange the equation to form a quadratic equation:
x^2 + 7x - 120 = 0
Factoring the Quadratic Equation
To solve the quadratic equation, we can try to factor it. If we can factor the equation, we can find the values of x that satisfy the equation. Let's try to factor the equation:
x^2 + 7x - 120 = (x + 15)(x - 8) = 0
Finding the Values of x
Now that we have factored the equation, we can find the values of x that satisfy the equation. We can set each factor equal to zero and solve for x:
x + 15 = 0 --> x = -15 (not possible, since the width cannot be negative)
x - 8 = 0 --> x = 8
Finding the Length
Now that we have found the value of x, which represents the width of the parking lot, we can find the length. We know that the length is 7 meters greater than the width, so we can write:
Length = x + 7 = 8 + 7 = 15
Conclusion
In this article, we have solved a problem involving a rectangular parking lot. We have found the length and the width of the parking lot, given that the length is 7 meters greater than the width and the area of the parking lot is 120 square meters. The width of the parking lot is 8 meters, and the length is 15 meters.
Final Answer
The final answer is:
- Width: 8 meters
- Length: 15 meters
Related Problems
If you are interested in solving more problems like this, here are some related problems:
- A rectangular garden has a length that is 5 meters greater than the width. The area of the garden is 180 square meters. Find the length and the width.
- A rectangular room has a length that is 3 meters greater than the width. The area of the room is 120 square meters. Find the length and the width.
- A rectangular field has a length that is 2 meters greater than the width. The area of the field is 240 square meters. Find the length and the width.
References
- [1] "Algebra" by Michael Artin
- [2] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
- [3] "Calculus" by Michael Spivak
Note: The references provided are for general information and are not directly related to the problem solved in this article.
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Introduction
In our previous article, we solved a problem involving a rectangular parking lot. We found the length and the width of the parking lot, given that the length is 7 meters greater than the width and the area of the parking lot is 120 square meters. In this article, we will answer some frequently asked questions related to the problem.
Q&A
Q: What is the formula for the area of a rectangle?
A: The formula for the area of a rectangle is:
Area = Length × Width
Q: How do I find the length and the width of a rectangle if I know the area and the difference between the length and the width?
A: To find the length and the width of a rectangle, you can use the following steps:
- Let the width be x.
- The length is x + the difference between the length and the width.
- Use the formula for the area of a rectangle to set up an equation.
- Solve the equation to find the value of x.
- Find the length by adding the difference between the length and the width to the value of x.
Q: What if the difference between the length and the width is negative?
A: If the difference between the length and the width is negative, it means that the width is greater than the length. In this case, you can simply swap the values of the length and the width.
Q: Can I use the quadratic formula to solve the equation?
A: Yes, you can use the quadratic formula to solve the equation. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 7, and c = -120. Plugging these values into the quadratic formula, you get:
x = (-(7) ± √((7)^2 - 4(1)(-120))) / 2(1) x = (-7 ± √(49 + 480)) / 2 x = (-7 ± √529) / 2 x = (-7 ± 23) / 2
Solving for x, you get two possible values:
x = (-7 + 23) / 2 = 8 x = (-7 - 23) / 2 = -15
Since the width cannot be negative, the correct value of x is 8.
Q: Can I use a calculator to solve the equation?
A: Yes, you can use a calculator to solve the equation. Simply plug in the values of a, b, and c into the quadratic formula, and the calculator will give you the solutions.
Q: What if I get a negative value for the width?
A: If you get a negative value for the width, it means that the width is not a real number. In this case, you can try to find the length and the width using a different method, such as graphing the equation or using a different formula.
Conclusion
In this article, we have answered some frequently asked questions related to the problem of finding the length and the width of a rectangle. We have discussed the formula for the area of a rectangle, how to find the length and the width using the quadratic formula, and what to do if you get a negative value for the width.
Final Answer
The final answer is:
- Width: 8 meters
- Length: 15 meters
Related Problems
If you are interested in solving more problems like this, here are some related problems:
- A rectangular garden has a length that is 5 meters greater than the width. The area of the garden is 180 square meters. Find the length and the width.
- A rectangular room has a length that is 3 meters greater than the width. The area of the room is 120 square meters. Find the length and the width.
- A rectangular field has a length that is 2 meters greater than the width. The area of the field is 240 square meters. Find the length and the width.
References
- [1] "Algebra" by Michael Artin
- [2] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
- [3] "Calculus" by Michael Spivak
Note: The references provided are for general information and are not directly related to the problem solved in this article.