tha are of a rectangular wall of a barn is 72 square feet. its length is 10 feet longer than twice its width. find the length and width of the wall of the barn

2x + 10=72....

2x=62
x=31

Oh yeah I almost forgot you can check my putting the X in

2*31+10=72
62+10
72=72

Step 1: Let's assume the width of the wall is represented by "w" feet.

Step 2: According to the problem, the length of the wall is 10 feet longer than twice its width, so the length can be represented by (2w + 10) feet.

Step 3: The formula to calculate the area of a rectangle is length multiplied by width. Therefore, we have:

Area = Length * Width
72 = (2w + 10) * w

Step 4: Simplify the equation by multiplying:

72 = 2w^2 + 10w

Step 5: Rearrange the equation to form a quadratic equation:

2w^2 + 10w - 72 = 0

Step 6: Solve the quadratic equation. You can simplify it by dividing both sides by 2:

w^2 + 5w - 36 = 0

Step 7: Factorize the quadratic equation:

(w + 9)(w - 4) = 0

Step 8: Set each factor equal to zero:

w + 9 = 0 OR w - 4 = 0

Step 9: Solve for w:

w = -9 OR w = 4

Since the width cannot be negative, we discard the solution w = -9.

Step 10: Therefore, the width of the wall is 4 feet.

Step 11: To find the length, substitute the value of width (w = 4) into the equation for length:

Length = 2w + 10
Length = 2 * 4 + 10
Length = 8 + 10
Length = 18

Step 12: Therefore, the length of the wall is 18 feet.

So, the dimensions of the wall of the barn are:
Width = 4 feet
Length = 18 feet

To find the length and width of the wall of the barn, we can use algebra. Let's assign variables to represent the dimensions of the wall:

Let's say the width of the wall is "w" feet.
According to the problem, the length is 10 feet longer than twice the width. So the length can be represented as "(2w + 10)" feet.

The area of a rectangle is given by the formula: Area = Length x Width.

Given that the area of the wall is 72 square feet, we can set up the equation:

72 = (2w + 10) × w.

To solve this equation, we can distribute the w to both terms inside the parentheses:

72 = 2w² + 10w.

Next, let's rearrange the equation to bring all terms to one side:

2w² + 10w - 72 = 0.

Now, we need to solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:

w = (-b ± sqrt(b² - 4ac)) / (2a).

For our equation, a = 2, b = 10, and c = -72. Plugging these values into the quadratic formula:

w = (-10 ± sqrt(10² - 4 · 2 · -72)) / (2 · 2).

Simplifying further:

w = (-10 ± sqrt(100 + 576)) / 4.

w = (-10 ± sqrt(676)) / 4.

w = (-10 ± 26) / 4.

Now we have two possible values for the width. Let's calculate both options:

Option 1: w = (-10 + 26) / 4 = 16 / 4 = 4.

Option 2: w = (-10 - 26) / 4 = -36 / 4 = -9.

Since we are dealing with dimensions, the width cannot be negative. So we discard the negative solution.

Therefore, the width (w) of the wall is 4 feet.

To find the length, we substitute the value of width (w = 4) into the equation (length = 2w + 10):

length = 2w + 10 = 2(4) + 10 = 8 + 10 = 18.

Therefore, the length of the wall is 18 feet.

In conclusion, the length of the wall of the barn is 18 feet and the width is 4 feet.