A rectangular field is four times as long as it is wide. If the perimeter of the field is 750 feet, what are the dimensions of the field?
Let w represent the width.
2 (4w) + 2w = 750
8w + 2w = 750
10w = 750
w = 75
Let's L=4w
2(L+w)=P
2(4w+w)=750
8w+2w=750
10w=750
W=75
So the width of the field is 75 feet.
To find the length, we can use L=4w.
L=4(75)
L=300
So the dimensions of the field are 75 feet by 300 feet.
To find the dimensions of the rectangular field, we can set up an equation based on the given information. Let's assume that the width of the field is x feet.
According to the given information, the length of the field is four times the width, so the length would be 4x feet.
The formula to calculate the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Using this formula, we can set up the equation:
750 = 2(4x) + 2x
Simplifying the equation, we get:
750 = 8x + 2x
Combining like terms:
750 = 10x
To isolate x, we divide both sides of the equation by 10:
750/10 = x
75 = x
Therefore, the width of the field is 75 feet.
The length of the field is four times the width, so:
Length = 4 x 75 = 300 feet.
Thus, the dimensions of the rectangular field are 75 feet by 300 feet.