A new Outdoor Recreation Center is being built in Erie. The perimeter of the rectangular playing field is 450 yards. The length of the field is 3 yards less than triple the width. What are the dimensions of the playing field? Show your work.
2 (L + W) = 450 ... L + W = 225
L + 3 = W
substituting ... L + L + 3 = 225
solve for L , then subtitute back to find W
thank you, but im still confused. could you help me out with the last bit? i cant figure out the width
To find the dimensions of the playing field, we can use the given information about the perimeter and the relationship between the length and the width.
Let's let the width of the field be represented by "W" in yards. According to the given information, the length of the field is 3 yards less than triple the width, which can be expressed as (3W - 3).
The formula for the perimeter of a rectangle is 2(length + width). In this case, we are given that the perimeter is 450 yards. Therefore, we can set up the equation:
2((3W - 3) + W) = 450
Simplifying the equation:
2(4W - 3) = 450
8W - 6 = 450
8W = 456
W = 456/8
W = 57
Now that we have found the width of the field to be 57 yards, we can substitute this value back into the equation for the length:
Length = 3W - 3
Length = 3(57) - 3
Length = 171 - 3
Length = 168
Therefore, the dimensions of the playing field are 168 yards by 57 yards.