If the area of a square is 9x2-12xy+4y2, what is the perimeter of the square in terms of x and y.
*its 9x squared and 4y squared
i have several problems like this on my homework if you show me how to do this one im sure i could figure out the rest
Since the 4 sides are equal:
A = S^2 = 9X^2 - 12XY + 4Y^2,
The trinomial is a perfect square:
S^2 = (3x - 2y)^2,
Take the sqrt of both sides:
S = 3X - 2Y = Length of each side,
p = 4*s = 4(3x -2y), or 12x - 8y.
To find the perimeter of a square, we need to know the length of one of its sides.
Given that the area of the square is 9x^2 - 12xy + 4y^2, we can rewrite it as the square of a binomial:
(3x - 2y)^2
This indicates that the length of one side of the square is equal to 3x - 2y.
The perimeter of a square is calculated by summing the lengths of all four sides. Since all sides of the square are equal, we multiply the length of one side by 4:
Perimeter = 4 * (3x - 2y)
Therefore, the perimeter of the square in terms of x and y is 12x - 8y.
To find the perimeter of a square, we need to know the length of one side of the square. However, in this case, we are given the area of the square, which is expressed as 9x^2 -12xy + 4y^2.
To find the length of one side, we need to take the square root of the given area. Let's simplify the expression first:
9x^2 - 12xy + 4y^2
This expression can be factored into a perfect square trinomial:
(3x - 2y)^2
Now, we can take the square root of this expression to find the side length:
√(3x - 2y)^2 = 3x - 2y
Therefore, the length of one side of the square is 3x - 2y.
Now that we know the length of one side, we can find the perimeter of the square by multiplying the side length by 4:
Perimeter = 4 * (3x - 2y)
= 12x - 8y
Hence, the perimeter of the square in terms of x and y is 12x - 8y.