The perimeter of the rectangle playing field is 342 yards balance of the bill is 9 yards less than triple the way what are the dimensions of the playing field
Huh ??
Let's break down the problem step-by-step:
Step 1: Understand the problem.
We are given that the perimeter of the rectangle playing field is 342 yards, and the length is 9 yards less than triple the width.
Step 2: Assign variables.
Let's assign the following variables:
- Width = W
- Length = 3W - 9
Step 3: Calculate the perimeter.
The formula for the perimeter of a rectangle is given as: P = 2(length + width)
Given that the perimeter is 342 yards, we can write the equation as:
342 = 2((3W - 9) + W)
Step 4: Simplify the equation.
342 = 2(4W - 9)
342 = 8W - 18
342 + 18 = 8W
360 = 8W
Step 5: Solve for W.
Divide both sides of the equation by 8:
360/8 = W
45 = W
Step 6: Calculate the length.
Using the value of W, we can calculate the length, which is 3W - 9:
Length = 3(45) - 9
Length = 135 - 9
Length = 126
Step 7: Check the dimensions.
To check if the dimensions are correct, we can calculate the perimeter:
Perimeter = 2(Length + Width)
Perimeter = 2(126 + 45)
Perimeter = 2(171)
Perimeter = 342
The dimensions of the playing field are:
Width = 45 yards
Length = 126 yards
To find the dimensions of the playing field, we need to set up an equation based on the information given.
Let's start by assigning variables to the dimensions of the rectangle. Let's call the length "l" and the width "w".
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
We are given that the perimeter of the playing field is 342 yards:
342 = 2 * (l + w)
Now, let's move on to the second piece of information. We are told that the balance of the bill (which I assume refers to the area of the playing field) is 9 yards less than triple the width. This can be written as:
l * w = (3w) - 9
So now we have a system of two equations:
1) 342 = 2 * (l + w)
2) l * w = (3w) - 9
We can use these equations to solve for the dimensions of the playing field. First, we can simplify equation 1 by dividing both sides by 2:
171 = l + w
To solve for one variable in terms of the other, we can use equation 1 to express l in terms of w:
l = 171 - w
Now, substitute this expression for l in equation 2:
(171 - w) * w = (3w) - 9
Expanding the equation and simplifying:
171w - w^2 = 3w - 9
Rearranging to bring all terms to one side:
w^2 + 168w - 9 = 0
Now we have a quadratic equation. We can solve for w using factoring, completing the square, or the quadratic formula.
However, in this case, the quadratic equation does not factor easily, so let's solve it using the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 1, b = 168, and c = -9. Plugging these values into the formula:
w = (-168 ± √(168^2 - 4*1*(-9))) / (2*1)
w = (-168 ± √(28,224 + 36)) / 2
w = (-168 ± √28,260) / 2
Now we need to calculate the square root:
w = (-168 ± 168.24) / 2
This gives us two possible values for w:
w1 = (-168 + 168.24) / 2 ≈ 0.12
w2 = (-168 - 168.24) / 2 ≈ -168.12
Since width cannot be negative in this context, we disregard the second value.
Now, substitute w = 0.12 back into equation 1 to solve for l:
171 = l + 0.12
l = 171 - 0.12 ≈ 170.88
So, the dimensions of the playing field are approximately: length = 170.88 yards and width = 0.12 yards. However, since a width of 0.12 yards is unrealistic, it's important to double-check the calculations and ensure the accuracy of the provided information.
I think you want to say that the width is w. So, the length is 3w-9. If so, then you have
2(w + 3w-9) = 342
Now just solve for w.