The area of a square field is represented by the trinomial x^2-10x+25. Write an expression that would represent the perimeter of the field.
A = x^2 - 10x + 25 = (x - 5)(x - 5)
A = Lw
L = (x - 5), w = (x - 5)
P = 2w + 2L
P = 2(x - 5) + 2(x - 5)
P = 2x - 10 + 2x - 10
P = 4x - 20
To find the expression representing the perimeter of the square field, we need to know that the perimeter of a square is given by P = 4s, where "s" represents the length of each side.
In this case, we can determine the length of the side by taking the square root of the area, since the area of a square is equal to the square of its side length.
So, let's start by finding the square root of the trinomial x^2 - 10x + 25:
√(x^2 - 10x + 25)
Now, let's simplify this expression:
√[(x - 5)(x - 5)]
The expression inside the square root can be factorized into (x - 5)(x - 5).
So, the square root simplifies to:
x - 5
Now, we can substitute this expression for the side length "s" in the perimeter formula:
P = 4s = 4(x - 5)
Hence, the expression representing the perimeter of the field is 4(x - 5).