your are building a soccer field. the length has to be 30 m longer than the width, and the total perimeter must be between 320i m and 360 m.
width ---- x m
length ---- x+30
320 < 2x + 2(x+30) < 360
320 < 4x + 60 < 360
260 < 4x < 300
65 < x < 75
To build a soccer field with specific length and width requirements, as well as perimeter constraints, we can follow the steps below:
Step 1: Define the width of the soccer field.
Let's assume the width of the field is "x" meters.
Step 2: Determine the length of the soccer field
Since the length must be 30 meters longer than the width, we add 30 to the width: x + 30.
Step 3: Calculate the perimeter of the soccer field
The perimeter of a rectangle is given by the formula: P = 2(length + width).
For our soccer field, the perimeter should be between 320 and 360 meters.
So, we can set up the inequality as follows: 320 ≤ 2(x + (x + 30)) ≤ 360.
Step 4: Solve the inequality
Let's simplify the inequality: 320 ≤ 2(2x + 30) ≤ 360.
Now, we can divide the inequality by 2: 160 ≤ 2x + 30 ≤ 180.
Next, subtract 30 from the inequality: 130 ≤ 2x ≤ 150.
Finally, divide the inequality by 2: 65 ≤ x ≤ 75.
So, the width of the soccer field should be within the range of 65 meters to 75 meters.
Step 5: Calculate the length of the soccer field
Using the width calculated in the previous step, we can determine the length by adding 30 to the width.
Therefore, the length of the soccer field would be in the range of 65 + 30 = 95 meters to 75 + 30 = 105 meters.
To summarize, the soccer field should have a width ranging from 65 to 75 meters and a length ranging from 95 to 105 meters.