A rectangular field is 35 m longer than it is wide. The length of the fence around the
perimeter of the field is 290 m. What are the dimensions (length and width) of the
fence?
Can you explain to me please
P = 2L + 2W
390 = 2(W + 35) + 2W
390 = 2W + 70 + 2W
320 = 4W
80 = W
To solve this problem, let's set up an equation based on the given information.
Let's assume that the width of the field is "x" meters.
According to the problem, the length of the field is 35 meters longer than its width, which means the length is "x + 35" meters.
The formula for the perimeter of a rectangle is P = 2L + 2W, where P represents the perimeter, L represents the length, and W represents the width.
In this case, the perimeter is given as 290 meters, so we can set up the equation:
290 = 2(x + 35) + 2x
Now, let's solve for x:
290 = 2x + 70 + 2x
290 = 4x + 70
220 = 4x
x = 55
The width of the field is 55 meters.
To find the length, we can substitute this value back into the equation:
L = x + 35
L = 55 + 35
L = 90
The length of the field is 90 meters.
Therefore, the dimensions of the fence are 90 meters (length) and 55 meters (width).
To solve this problem, we can set up two equations based on the given information.
Let's assume the width of the field is x meters.
According to the problem statement, the length of the rectangular field is 35 m longer than its width. Therefore, the length would be (x + 35) meters.
The first equation can be derived from the given perimeter of the field:
Perimeter = 2 * (Length + Width)
290 = 2 * ((x + 35) + x)
Simplifying the equation:
290 = 2 * (2x + 35)
Divide both sides of the equation by 2:
290/2 = 2x + 35
145 = 2x + 35
Subtract 35 from both sides of the equation:
145 - 35 = 2x
110 = 2x
Finally, divide both sides by 2 to isolate x:
110/2 = x
x = 55
The width of the field is 55 meters.
Substituting this value back into the equation for the length:
Length = Width + 35
Length = 55 + 35
Length = 90
Therefore, the width of the field is 55 meters, and the length is 90 meters.