a rectangular parking lot has a length that is 10 yards greater than the width. the area of the parking lot is 200 square yards.find the length and the width
the equation you use is:
200=w(10+w)
200=10w+w^2
w^2+10w-200 = 0
(w+20)(w-10)= 0
w = -20 or 10
it has to be positive so the answer is 10.
The width is 10 yards and the length is 20 yards
Let's start by assigning variables to the width and length of the rectangular parking lot.
Let's say the width of the parking lot is 'w' yards.
According to the given information, the length is 10 yards greater than the width, so the length can be represented as 'w + 10' yards.
The formula to calculate the area of a rectangle is:
Area = Length × Width
We know that the area is 200 square yards. Substituting the values we have:
200 = (w + 10) × w
Now, let's solve this equation to find the width (w) and then calculate the length (w + 10).
To solve the equation, we can start by simplifying it:
200 = w^2 + 10w
Rearranging the equation to bring all terms to one side:
w^2 + 10w - 200 = 0
Now we can solve this quadratic equation.
This equation can be factored as follows:
(w + 20)(w - 10) = 0
Setting each factor equal to zero:
w + 20 = 0 or w - 10 = 0
Solving each equation separately:
w + 20 = 0 --> w = -20 (disregard because the width cannot be negative)
w - 10 = 0 --> w = 10
Now we have the width, which is 10 yards. To find the length, we add 10 to the width:
Length = w + 10 = 10 + 10 = 20 yards
Therefore, the width of the parking lot is 10 yards, and the length is 20 yards.
To find the length and width of the rectangular parking lot, we can use the information provided in the problem.
Let's assume that the width of the parking lot is "w" yards. According to the problem, the length is 10 yards greater than the width, so we can represent the length as "w + 10" yards.
Now, we know that the area of a rectangle is given by the formula: Area = length x width.
So in this case, the area of the parking lot is given as 200 square yards.
Using the formula, we can set up the equation: (w + 10)w = 200.
Now, let's solve for w:
w^2 + 10w = 200
Rearranging the equation:
w^2 + 10w - 200 = 0
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's solve it by factoring:
(w - 10)(w + 20) = 0
This gives us two possible solutions for w:
w - 10 = 0 or w + 20 = 0
Solving each equation:
For w - 10 = 0, adding 10 to both sides, we get:
w = 10
For w + 20 = 0, subtracting 20 from both sides, we get:
w = -20
Since the width cannot be negative, we will discard the second solution.
Therefore, the width of the parking lot is 10 yards.
To find the length, we'll substitute the width value in our earlier equation:
Length = w + 10 = 10 + 10 = 20 yards.
Hence, the length of the parking lot is 20 yards and the width is 10 yards.