Find the length of the sides of a square if the number of square meters in it's area is 1.5 times the number of the meters in it's perimeter
To find the length of the sides of a square, we need to set up an equation based on the given information.
Let's assume that the length of one side of the square is represented by the variable 's'.
The area of a square is given by the formula A = s^2, and the perimeter is given by P = 4s.
According to the problem, the area of the square is 1.5 times the perimeter. So, we can write the equation as:
1.5P = A
Substituting the formulas for A and P, we get:
1.5(4s) = s^2
6s = s^2
Rearranging the equation:
s^2 - 6s = 0
Now we have a quadratic equation. To solve for 's', we can factor or use the quadratic formula.
Factoring the equation:
s(s - 6) = 0
Setting each factor equal to zero:
s = 0 or s - 6 = 0
Since the length of a side of a square cannot be zero, we disregard the first solution. Therefore, the only valid solution is:
s - 6 = 0
Solving for 's', we find:
s = 6
Hence, the length of each side of the square is 6 units.