The perimeter of a square is equal to its area plus four. What is the measure of one side of the square?
4s=s^2+4
s^2-4s+4=0
(s-2)(s-2)=0
s=2
Let's assume that the measure of one side of the square is represented by "x".
The formula for the perimeter of a square is given by P = 4 * x, where P is the perimeter and x is the length of one side.
The formula for the area of a square is given by A = x^2, where A is the area and x is the length of one side.
According to the given information, the perimeter is equal to the area plus four, so we can write the equation as: P = A + 4.
Substituting the formulas for the perimeter and area into the equation, we get: 4x = x^2 + 4.
Rearranging the equation, we have: x^2 - 4x + 4 = 0.
To solve this quadratic equation, we can use factoring or the quadratic formula.
Factoring the equation, we have: (x - 2)(x - 2) = 0.
This gives us two possible solutions: x - 2 = 0, which means x = 2.
Therefore, the measure of one side of the square is 2 units.
To find the measure of one side of the square, we need to set up an equation based on the given information.
Let's assume that the side length of the square is 's'. The perimeter of a square is calculated by multiplying the side length by 4, so the perimeter would be 4s.
According to the problem, the perimeter of the square is equal to its area plus four. The area of a square is calculated by squaring its side length, so the area would be s^2.
Putting this together, we have the equation:
4s = s^2 + 4
To solve this equation, we can rearrange it into a quadratic form:
s^2 - 4s + 4 = 0
Next, we can either factor the quadratic equation or use the quadratic formula to find the values of 's'. Factoring this equation, we obtain:
(s - 2)(s - 2) = 0
Therefore, s - 2 = 0, which leads to s = 2.
Hence, the measure of one side of the square is 2.