Find the area of a square given that the length of each of its sides is 1/4 the value of its area.
16?
That was my first thought but it seems to easy to be true!!!!
Let's assume the length of each side of the square is "s". According to the given information, we know that the length of each side is 1/4 the value of its area.
The area of a square is calculated by multiplying the length of one side by itself. Therefore, we have the equation:
s = (1/4) * (s^2)
To find the area of the square, we need to solve this equation for s.
First, let's eliminate the fraction by multiplying both sides of the equation by 4:
4s = s^2
Now, rearrange the equation to get it in the following form:
s^2 - 4s = 0
Factor out an "s" from the left-hand side:
s(s - 4) = 0
Now, we have two possible solutions for s: s = 0 or s - 4 = 0
However, the length of a side cannot be zero, so we can disregard s = 0.
We are left with s - 4 = 0, which gives us:
s = 4
Therefore, the length of each side is 4.
To find the area of the square, we square the length of one side:
Area = s^2 = 4^2 = 16 square units.
Hence, the area of the square is 16 square units.
To find the area of a square, we need to know the length of one of its sides. However, in this question, we are given that the length of each side is equal to 1/4 of the value of its area. Let's call the length of one side of the square "s".
Now, according to the given information, the length of one side is equal to 1/4 of the area. Mathematically, we can express this as:
s = (1/4) * Area
To find the area, we can substitute this expression into the formula for the area of a square. The formula for the area of a square is:
Area = s²
By substituting the expression for "s", we get:
Area = ((1/4) * Area)²
To solve this equation, let's simplify it step by step:
First, square both sides of the equation:
Area² = ((1/4) * Area)²
Area² = (1/16) * Area²
Next, multiply both sides of the equation by 16 to eliminate the fraction:
16 * Area² = 16 * (1/16) * Area²
16 * Area² = Area²
Now, subtract Area² from both sides of the equation:
16 * Area² - Area² = 0
15 * Area² = 0
Finally, divide both sides of the equation by 15 to get the value of Area²:
Area² = 0 / 15
Area² = 0
Since the area cannot be negative, we can conclude that the area of the square is zero.
Therefore, the area of the square is 0.