Suppose that the area of a square is forty-one times its perimeter. Find the length of a side of the square.
41(x+x+x+x)=x^2
since the area of a square is forty-one times its perimeter, I multiply 41 on the perimeter side to set the perimeter equal to the area
solve for x. you'll get two answers. eliminate the one that is equal to zero since a measure of length cannot equal to zero!
thank you ! I solved it
To find the length of a side of the square, let's represent the side length of the square by the variable '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 statement, the area of the square is forty-one times its perimeter. Mathematically, this can be written as:
A = 41P
Substituting the formulas for area and perimeter:
s^2 = 41(4s)
Now, let's simplify this equation:
s^2 = 164s
Rearranging the equation:
s^2 - 164s = 0
Factoring out the common factor s:
s(s - 164) = 0
Now, we have two possibilities:
1) s = 0: This is not a valid solution because we are looking for the length of a side, which cannot be zero.
2) s - 164 = 0: Solving for s, we find:
s = 164
Therefore, the length of a side of the square is 164 units.