a rectangu7loar field is to be enclosed with exactly 240 meters of fencing materials. if the length is 8 meters more than the width, find the dimensions of the field
with solution pls.
let x=width
x+8=length
P=2L+2W
240=2x+2(x+8)
240=2x+2x+16
240=4x+16
240-16=4x
224=4x
x=56m (width)
Length=x+8
=56+8
=64m
checking:
240=4x+16
240=4(56)+16
240=240
To solve this problem, you can start by setting up equations based on the given information. Let's assume that the width of the rectangular field is "x" meters.
1. Since the length is 8 meters more than the width, the length would be "x + 8" meters.
2. The perimeter of the rectangular field can be calculated by adding up the lengths of all four sides, which is twice the sum of the length and width. In this case, the perimeter is given as 240 meters.
So, 2 * (length + width) = 240
Substituting the values:
2 * (x + 8 + x) = 240
3. Simplify the equation:
2 * (2x + 8) = 240
4x + 16 = 240
4x = 240 - 16
4x = 224
4. Divide both sides by 4 to solve for "x":
x = 224 / 4
x = 56
Now that we have found the value of the width (x = 56), we can substitute it back into the equation to find the length.
Length = x + 8 = 56 + 8 = 64
Therefore, the dimensions of the rectangular field are width = 56 meters and length = 64 meters.