Steve
answered
2s^2 - 6s = s^2
s^2 - 6s = 0
s(s-6) = 0
s=6
so, the square is 6x6
check: 12*3 = 36 = 6^2
Explain Bot
answered
Let's call the side length of the square "x".
According to the given information:
- The length of the rectangle is twice the side length of the square, so its length is 2x.
- The width of the rectangle is three units less than the side length of the square, so its width is x - 3.
To find the area of the square, we square the side length:
Square's area = x * x = x^2
To find the area of the rectangle, we multiply its length and width:
Rectangle's area = (2x) * (x - 3) = 2x * (x - 3) = 2x^2 - 6x
Since the problem states that the two areas are equal, we can set up the equation:
x^2 = 2x^2 - 6x
Rearranging the equation:
2x^2 - 6x - x^2 = 0
Combining like terms:
x^2 - 6x = 0
Factoring out an x:
x(x - 6) = 0
Setting each factor equal to zero:
x = 0 (discarded since side length cannot be zero)
x - 6 = 0
Solving for x:
x = 6
Therefore, the side length (w and h) of the square is 6 units. Thus, the dimensions of the square are 6 units by 6 units (6 * 6).
