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A rectangular parking lot that is 3 feet longer than it is wide has an area of 550 square feet. How many feet long is the parking lot?
- a)19
- b)20
- c)22
- d)25
- e)28
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A rectangular parking lot that is 3 feet longer than it is wide has an...
To solve this problem, we need to use the given information to set up an equation and solve for the length of the parking lot. Let's break down the problem step by step:
1. Given information:
- The parking lot is rectangular.
- The length of the parking lot is 3 feet longer than its width.
- The area of the parking lot is 550 square feet.
2. Let's assume the width of the parking lot as "x" feet.
- Therefore, the length of the parking lot is "x + 3" feet.
3. The formula for the area of a rectangle is:
- Area = Length * Width
4. Substituting the given information into the formula:
- Area = (x + 3) * x = 550
5. Simplifying the equation:
- x^2 + 3x = 550
6. Rearranging the equation to make it easier to solve:
- x^2 + 3x - 550 = 0
7. Now, we can solve the equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring.
8. Factoring the quadratic equation:
- (x + 25)(x - 22) = 0
9. Setting each factor equal to zero and solving for x:
- x + 25 = 0 or x - 22 = 0
- x = -25 or x = 22
10. Since the width cannot be negative, we discard the negative value and conclude that the width of the parking lot is 22 feet.
11. Finally, we can find the length of the parking lot by adding 3 to the width:
- Length = 22 + 3 = 25 feet
Therefore, the length of the parking lot is 25 feet, which corresponds to option D.
1. Given information:
- The parking lot is rectangular.
- The length of the parking lot is 3 feet longer than its width.
- The area of the parking lot is 550 square feet.
2. Let's assume the width of the parking lot as "x" feet.
- Therefore, the length of the parking lot is "x + 3" feet.
3. The formula for the area of a rectangle is:
- Area = Length * Width
4. Substituting the given information into the formula:
- Area = (x + 3) * x = 550
5. Simplifying the equation:
- x^2 + 3x = 550
6. Rearranging the equation to make it easier to solve:
- x^2 + 3x - 550 = 0
7. Now, we can solve the equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring.
8. Factoring the quadratic equation:
- (x + 25)(x - 22) = 0
9. Setting each factor equal to zero and solving for x:
- x + 25 = 0 or x - 22 = 0
- x = -25 or x = 22
10. Since the width cannot be negative, we discard the negative value and conclude that the width of the parking lot is 22 feet.
11. Finally, we can find the length of the parking lot by adding 3 to the width:
- Length = 22 + 3 = 25 feet
Therefore, the length of the parking lot is 25 feet, which corresponds to option D.
Community Answer
A rectangular parking lot that is 3 feet longer than it is wide has an...
If a rectangular parking lot has a length, l, that is 3 feet longer than its width, w, then l = 3 + w, or w = l - 3. The area of a rectangle is equal to its length times it width, or A = Iw. Since the area of this parking lot is 550, Iw = 550. Substituting (l - 3) for
550 = l(l - 3) =
550 = l2 - 3l
l2 - 3l - 550 = 0.
To solve for l, factor the quadratic equation to get (l + 22)(l - 25) = 0, making l = -22 or l = 25. Since negative values for length do not make sense in this context, the length is 25.
550 = l(l - 3) =
550 = l2 - 3l
l2 - 3l - 550 = 0.
To solve for l, factor the quadratic equation to get (l + 22)(l - 25) = 0, making l = -22 or l = 25. Since negative values for length do not make sense in this context, the length is 25.
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A rectangular parking lot that is 3 feet longer than it is wide has an area of 550 square feet. How many feet long is the parking lot?a)19b)20c)22d)25e)28Correct answer is option 'D'. Can you explain this answer?
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