The Area of a square is numerically less than six times its side list some squares in which this happen
s² < 6 s ... s < 6
any square with a side length less than 6
To find squares where the area is numerically less than six times its side, we need to express this condition mathematically.
Let's suppose the side length of the square is "s". The area of the square can be calculated as s^2.
According to the given condition, the area is less than six times the side length: s^2 < 6s.
To determine some squares that satisfy this condition, we can solve the inequality mathematically.
Step 1: Rearrange the inequality:
s^2 - 6s < 0
Step 2: Factorize the quadratic equation:
s(s - 6) < 0
Step 3: Identify the critical values (values where the inequality changes):
s = 0 and s - 6 = 0
Step 4: Create a number line and mark the critical values on it:
-infinity | 0 | 6 | +infinity
Step 5: Test intervals to find the solution:
- Choose a value less than 0 (e.g., -1):
-1(-1 - 6) = 7, which is greater than 0 (false).
- Choose a value between 0 and 6 (e.g., 3):
3(3 - 6) = -9, which is less than 0 (true).
- Choose a value greater than 6 (e.g., 7):
7(7 - 6) = 7, which is greater than 0 (false).
Step 6: Determine the solution:
The inequality is true for values between 0 and 6. Therefore, the squares that satisfy the given condition have side lengths between 0 and 6. However, note that a side length of 0 is not practically possible for a square since a square must have a positive length. So, the squares with side lengths between 0 and 6 (excluding 0) would meet the condition.
For example, squares with side lengths of 1, 2, 3, 4, and 5 would all have areas less than six times their side lengths.