Find the area of a square whose side length is 1/4 the value of its area
16
Let's call the side length of the square "s". The area of a square is given by the formula A = s^2.
We are given that the side length is 1/4 the value of its area. Mathematically, this can be written as s = (1/4)A.
Substituting this expression for s into the formula for area, we have:
A = ((1/4)A)^2
Expanding the right-hand side:
A = (1/16)A^2
To solve for A, we can multiply both sides of the equation by 16 to get rid of the fraction:
16A = A^2
Rearranging this equation into quadratic form:
A^2 - 16A = 0
Factoring out the common factor of A:
A(A - 16) = 0
Now we can set each factor equal to zero and solve for A:
A = 0 or A - 16 = 0
Since the area cannot be zero, we have:
A - 16 = 0
A = 16
Therefore, the area of the square is 16 square units.
To find the area of a square, you need to know the length of its side. In this case, let's assume the side length of the square is ‘x’.
According to the given information, the side length of the square is equal to 1/4 of its area.
This can be written as:
x = (1/4) * (x^2)
To solve this equation, we can simplify:
4x = x^2
Rearranging the equation, we get:
x^2 - 4x = 0
Now, let's factor the equation:
x(x - 4) = 0
From this equation, we can see that there are two possible solutions: x = 0 and x = 4. Since the side length of a square cannot be zero, we can conclude that x = 4 is the solution.
Therefore, the side length of the square is 4.
Now, to find the area of the square, we can use the formula:
Area = side length squared
Area = 4^2 = 16 square units.
Hence, the area of the square is 16 square units.