Suppose that the area of a square is forty-one times its perimeter. Find the length of a side of the square.
All I can think of is that P=4s and A=s^2
thanks for any help
41 * 4s = s^2
Solve for s.
To solve this problem, we can set up an equation using the given information.
Let's assume that the side length of the square is 's'.
In a square, the perimeter is given by P = 4s (as you correctly mentioned).
The area of a square is A = s^2.
The problem states that the area of the square is forty-one times its perimeter. Mathematically, we can express this as:
A = 41P
Substituting the values for A and P, we get:
s^2 = 41 * 4s
Now, we can simplify this equation:
s^2 = 164s
Next, let's rearrange the equation to isolate the side length 's'.
s^2 - 164s = 0
Factoring out the 's' on the left side:
s(s - 164) = 0
This equation will be true if either s = 0 or s - 164 = 0. However, a square with a side length of zero does not make sense in this context, so we can discard s = 0.
Solving s - 164 = 0, we find:
s = 164
Therefore, the length of a side of the square is 164 units.
Remember to always check your answer!