The area of a rectangular wall of a barn is 24 square feet. Its length is 8 feet longer than twice its width. Find the length and width of the wall of the barn
Width = X Ft.
Length = (2x+8) Ft.
x*(2x+8) = 24Sq. Ft.
2x^2 + 8x = 24
Divide both sides by 2:
x^2 + 4x = 12
x^2 + 4x - 12 = 0.
(x-2)(x+6) = 0
x - 2 = 0
X = 2 = Width.
x + 6 = 0
X = -6. Negative value not valid.
2x+8 = 2*2 + 8 = 12 = Length.
Well, well, well, it sounds like someone needs my clown-tastic help! Let's solve this mystery together, shall we?
Let's say the width of the wall is x. According to the problem, the length is 8 feet longer than twice the width, which means the length is (2x + 8).
Now, my math skills are as sharp as my clown nose, so let's set up an equation:
Area = Length × Width
Substituting the values we found, we get:
24 = (2x + 8) × x
Simplifying, we have:
24 = 2x^2 + 8x
To make our equation easier to handle, let's move everything to one side of the equation:
2x^2 + 8x - 24 = 0
Now, here comes the fun part – let's solve this quadratic equation! Or we could try juggling, but solving it seems more productive.
Using our clown powers, we can either factor the quadratic equation or use the quadratic formula to find the values of x. Let's stick to the formula for this one:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in our values for this equation, we get:
x = (-8 ± √(8^2 - 4 * 2 * -24)) / (2 * 2)
Now, let's simplify this expression:
x = (-8 ± √(64 + 192)) / 4
x = (-8 ± √256) / 4
x = (-8 ± 16) / 4
So, we have two possible values for x:
x1 = (-8 + 16) / 4 = 2
x2 = (-8 - 16) / 4 = -6
Now, since we can't have a negative width for our barn wall (that would be quite shocking, wouldn't it?), we discard the negative value and stick with x = 2.
So, the width of the wall is 2 feet. Now let's find the length:
Length = 2x + 8
Length = 2(2) + 8
Length = 4 + 8
Length = 12
Voilà! The width of the wall is 2 feet, and the length is 12 feet. Now you'll have a perfectly rectangular barn wall to clown around with!
Let's assume the width of the wall is represented by 'W' feet.
According to the given information, the length of the wall is 8 feet longer than twice its width. We can represent this as: Length = 2W + 8.
The area of the rectangular wall is given as 24 square feet. We can use the formula for the area of a rectangle, which is length multiplied by width (A = L × W).
Substituting the values into the formula, we have 24 = (2W + 8) × W.
To solve this equation for W, we can distribute the W on the right side of the equation: 24 = 2W^2 + 8W.
Rearranging the equation to set it equal to zero, we have: 2W^2 + 8W - 24 = 0.
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's factorize the equation by taking out the common factor of 2: 2(W^2 + 4W - 12) = 0.
Now we have: W^2 + 4W - 12 = 0.
To factorize further, we need to find two numbers that multiply to -12 and add up to +4. These numbers are +6 and -2.
Therefore, we can rewrite the equation as (W + 6)(W - 2) = 0.
Setting each factor equal to zero, we have two possible solutions for W: W + 6 = 0 (which gives W = -6) or W - 2 = 0 (which gives W = 2).
Since a negative length is not meaningful in this context, we can ignore the negative solution.
So, the width of the wall is 2 feet.
To find the length, we can substitute the value of W back into the equation for the length: Length = 2W + 8.
Substituting W = 2, we get Length = 2(2) + 8 = 4 + 8 = 12.
Therefore, the length of the wall is 12 feet.
In conclusion, the width of the wall is 2 feet and the length of the wall is 12 feet.
To find the length and width of the wall of the barn, we can set up an equation based on the given information.
Let's denote the width of the wall as "w" feet.
According to the problem, the length of the wall is 8 feet longer than twice its width, which can be written as (2w + 8) feet.
The formula for the area of a rectangle is the product of its length and width, which gives us the equation:
Area = Length x Width
Substituting the given values, we have:
24 = (2w + 8)w
Now, let's solve this equation to find the values of "w" and (2w + 8).
To do that, we can rearrange the equation and set it equal to zero:
0 = 2w^2 + 8w - 24
Next, we can factorize the quadratic equation:
0 = 2(w^2 + 4w - 12)
0 = 2(w + 6)(w - 2)
To solve for "w," we set each factor equal to zero and solve for "w":
w + 6 = 0 --> w = -6 (Discard this value since width cannot be negative in this context)
w - 2 = 0 --> w = 2
Therefore, the width of the wall is 2 feet.
To find the length, we can substitute the value of "w" into our equation:
Length = 2w + 8 = 2(2) + 8 = 4 + 8 = 12
Hence, the length of the wall is 12 feet.
In conclusion, the width of the wall is 2 feet and the length is 12 feet.