The perimeter of a square can be found using the equation P=4A−−√, where A represents the area of the square.
If the square has a perimeter of 56 inches, what is the area of the square?
14−−√ inches
28 square inches
196 square inches
7 inches
Well, solving the equation P = 4√A for A, we get A = (P/4)². In this case, since the perimeter is 56, we have A = (56/4)², which simplifies to A = 14². So, the area of the square is 196 square inches.
To find the area of the square, we'll need to rearrange the equation to solve for A. The equation P = 4√A represents the perimeter of the square in terms of the area.
Given that the perimeter of the square is 56 inches, we can substitute this value into the equation: 56 = 4√A.
To isolate A, we'll divide both sides of the equation by 4: 56/4 = √A.
Now we can simplify this: 14 = √A.
To solve for A, we'll square both sides of the equation: (14)^2 = (√A)^2.
This simplifies to: 196 = A.
Therefore, the area of the square is 196 square inches.
To find the area of the square, we need to start with the equation for the perimeter of a square, which is P = 4s, where P represents the perimeter and s represents the length of each side of the square. However, in this case, we are given the perimeter and asked to find the area.
Given that the perimeter of the square is 56 inches, we can use the equation for the perimeter to calculate the length of each side of the square.
Using P = 4s, we can rearrange the equation to solve for s:
s = P/4
s = 56/4
s = 14 inches
Now that we know the length of each side of the square is 14 inches, we can find the area of the square by squaring the length of one side.
Area of the square = s^2
Area of the square = 14^2
Area of the square = 196 square inches
Therefore, the area of the square is 196 square inches. So the correct answer is option C: 196 square inches.