A garden has an area of 286ft^2. It's length is 9ft more than its width. What are the dimensions of the garden?
width --- x
length ---- x+9
x(x+9) = 286
x^2 + 9x - 286 = 0
(x - 13)(x + 22) = 0
x = 13 or x is a negative
the garden is 13 by 22
Ah, the age-old question of the dimensions of a garden. Let me put on my clown shoes and math hat for this one!
Let's assume that the width of the garden is 'x' feet. According to the information given, the length of the garden is 9 feet more than the width. So, the length can be represented as 'x + 9' feet.
Now, we know that the area of the garden is 286 square feet. The area of a rectangle is calculated by multiplying the length by the width. So, we have the equation:
(x)(x + 9) = 286
Now, let's solve this equation. But before we do, remember, math is serious business unless there's a clown involved!
Expanding the equation, we get:
x^2 + 9x = 286
Rearranging the equation, we get:
x^2 + 9x - 286 = 0
Now, let's factor this trinomial equation. Hmm... let me put on my thinking wig - viola!
(x - 13)(x + 22) = 0
So, we have two possible solutions:
x - 13 = 0, which means x = 13
x + 22 = 0, which means x = -22
Now, wait just a cotton candy minute! Negative dimensions for a garden don't make sense, do they? So, we'll disregard the negative solution.
Therefore, the width of the garden is 13 feet (sorry, not 13 clowns) and the length is 13 + 9 = 22 feet.
The dimensions of the garden are 13 feet by 22 feet. Ta-da! The mystery of the garden dimensions is solved, with a touch of clownery for fun.
Let's assume the width of the garden is x ft.
According to the given information, the length of the garden is 9 ft more than its width, so the length can be expressed as x + 9 ft.
Since the area of a rectangle is given by the formula: Area = Length × Width, we can set up the following equation:
x(x + 9) = 286
Expanding the equation:
x^2 + 9x = 286
Rearranging the equation in standard form:
x^2 + 9x - 286 = 0
This equation is quadratic, so we can solve it by factoring or using the quadratic formula. Factoring the equation gives us:
(x + 22)(x - 13) = 0
Setting each factor equal to zero gives us the possible values for x:
x + 22 = 0 or x - 13 = 0
Solving for x in each equation gives us:
x = -22 or x = 13
Since the width cannot be negative, the only valid solution is x = 13.
Therefore, the dimensions of the garden are:
Width = 13 ft
Length = x + 9 = 13 + 9 = 22 ft
To find the dimensions of the garden, we can set up an equation based on the information given.
Let's assume the width of the garden is 'w' feet. According to the given information, the length of the garden is 9 feet more than its width, so the length would be 'w + 9' feet.
The area of a rectangle is given by the formula: Area = length × width.
So, we have the equation:
Area = length × width
286 = (w + 9) × w
To solve this equation, we can expand the right side:
286 = w² + 9w
Now, we can rearrange the equation into a quadratic equation in standard form:
w² + 9w - 286 = 0
To solve the quadratic equation, we can factor it or use the quadratic formula:
w = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 1, b = 9, and c = -286.
Plugging in these values into the quadratic formula:
w = (-9 ± √(9² - 4(1)(-286))) / (2(1))
Simplifying further:
w = (-9 ± √(81 + 1144)) / 2
w = (-9 ± √(1225)) / 2
Since the dimensions of a garden cannot be negative, we can ignore the negative value within the square root:
w = (-9 + 35) / 2 or w = (-9 - 35) / 2
Simplifying:
w = 26 / 2 or w = -44 / 2
w = 13 or w = -22
Since the width of a garden cannot be negative, the width is 13 feet.
Now, we can find the length of the garden by adding 9 feet to the width:
length = width + 9 = 13 + 9 = 22
Therefore, the dimensions of the garden are 13 feet by 22 feet.