suppose that the area of a square is six times its perimeter. find the length of a side of the square
To find the length of a side of the square, we can start by setting up an equation based on the given information.
Let's assume the length of a side of the square is "s".
The area of a square is given by the formula A = s^2, and the perimeter is given by the formula P = 4s (since a square has four equal sides).
According to the problem, the area of the square is six times its perimeter. Translating this into an equation, we have:
A = 6P
Substituting the formulas for the area and perimeter, we get:
s^2 = 6(4s)
Simplifying the equation, we have:
s^2 = 24s
Next, we can rearrange the equation to solve for "s".
Dividing both sides of the equation by "s" (assuming s ≠ 0), we get:
s = 24
So, the length of a side of the square is 24 units.
P = 4s
A = s^2
s^2 = 6(4s)
Solve for s.