the perimeter of a rectangular field is 172 meters. double the width is 4 meters more than the length. find the area of the field.

2w -4 = l

2w +2l = 172

plug in for l and find w. then plug in w to find l

then a=lw

To find the area of the field, we first need to find the length and width of the rectangular field.

Let's assume the length of the field is "L" meters and the width is "W" meters.

Given that the perimeter of the rectangular field is 172 meters:
Perimeter = 2 * (Length + Width)

Substituting the given values, we have:
172 = 2 * (L + W)

Now, we are also given that double the width is 4 meters more than the length:
2W = L + 4

To solve this system of equations, we can use substitution.

Let's solve the second equation for L:
L = 2W - 4

Now substitute L into the first equation:
172 = 2 * (2W - 4 + W)

Simplify and solve for W:
172 = 2 * (3W - 4)
172 = 6W - 8
180 = 6W
W = 30

Substituting the value of W back into the equation L = 2W - 4:
L = 2 * 30 - 4
L = 60 - 4
L = 56

Therefore, the width (W) of the field is 30 meters and the length (L) is 56 meters.

To find the area of the rectangular field, we use the formula:
Area = Length * Width

Substituting the values:
Area = 56 * 30
Area = 1680 square meters

So, the area of the field is 1680 square meters.

To find the area of the rectangular field, we first need to determine the length and width of the field.

Let's assume the length of the field is "L" meters and the width is "W" meters.

From the given information, we can form two equations:

1) The perimeter of a rectangular field is given by: 2(L + W) = 172 meters
2) Double the width is 4 meters more than the length: 2W = L + 4

We can solve these equations to find the values of L and W.

From equation 2, we can express L in terms of W: L = 2W - 4

Substituting this value of L into equation 1, we get: 2((2W - 4) + W) = 172

Simplifying this equation: 2(3W - 4) = 172
6W - 8 = 172
6W = 180
W = 30

Now that we have the value of W, we can substitute it back into equation 2 to find the value of L: L = 2W - 4 = 2(30) - 4 = 56

Therefore, the length of the field is 56 meters and the width is 30 meters.

To find the area of the field, we multiply the length by the width:
Area = Length × Width = 56 meters × 30 meters = 1680 square meters.

Hence, the area of the rectangular field is 1680 square meters.