A rectangular field is four times as long as it is wide. If the perimeter is 470 yards what are the fields dimensions
Let's call the width of the field "w" yards.
According to the given information, the length of the field would be four times the width, so the length is 4w yards.
The formula for calculating the perimeter of a rectangle is P = 2L + 2W, where "P" is the perimeter, "L" is the length, and "W" is the width.
In this case, we know that the perimeter of the rectangle is 470 yards. So, we can set up the following equation:
470 = 2(4w) + 2w
Simplifying the equation, we get:
470 = 8w + 2w
Combining like terms, we have:
470 = 10w
Now, we can solve for "w" by dividing both sides of the equation by 10:
w = 470 / 10
w = 47
Therefore, the width of the field is 47 yards.
To find the length, we can substitute the value of "w" back into the equation for the length:
Length = 4w = 4 * 47 = 188 yards
So, the dimensions of the rectangular field are 188 yards by 47 yards.
To find the dimensions of the rectangular field when the perimeter is given, we can set up equations based on the given information.
Let's assume that the width of the rectangular field is "w" yards. According to the problem, the length is four times as long as the width, which means the length is 4w yards.
The formula for the perimeter of a rectangle is P = 2(length + width). Plugging in the known values, we have:
470 = 2(4w + w)
Now, let's solve for w.
470 = 2(5w)
470 = 10w
w = 470/10
w = 47
So, the width of the rectangular field is 47 yards.
To find the length, we can substitute this value back into the equation for the length: length = 4w
length = 4 * 47
length = 188
Therefore, the dimensions of the rectangular field are 47 yards (width) and 188 yards (length).
L = 4W
2L + 2W = 2(4W) + 2W = 470
Solve for W, then L.