Question

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Answer 1

Answer:

(x-6)

Step-by-step explanation:

To figure out the length of one side you need to first understand that to find the area you must use the formula A = l x w. Since the shape is a square, the side length should be the same for all sides. For this specific problem, all you would need to do is factor $x^2-12x+36$.

To factor  $x^2-12x+36$, you need to determine what two numbers add together to get -12and multiply to 36. These two numbers are -6. You would then need to fill in the blanks in (x+_)(x+_) with -6 and -6 to get (x-6)(x-6). Since it is only asking for one side, the answer would be (x-6)

Answer 2

Answer:

Side length = x - 6

Step-by-step explanation:

x² - 12x + 36      The expression for the area of the square

Remember the formula for area of a square is A = s² (Area is side squared).

s² = s x s

To find the length of one side, we need to change x² - 12x + 36 into an expression with two factors multiplying each other. This is done by factoring.

x² - 12x + 36 is a special type of trinomial called a perfect trinomial. To factor perfect trinomials, follow this rule:

ax² ± bx + c = (√(ax²) ± √(c))² = (√(ax²) ± √(c)) (√(ax²) ± √(c))

Take the square root of the first and last terms, then take the positive/negative sign of the middle term.

Square root of first term: √x² = x

Square root of last term: √36 = 6

Sign of middle term: (-) negative

x² - 12x + 36 = (x - 6)² = (x - 6)(x - 6)

Apply the formula for area to the factored form.

A = s² = (x - 6)²

Since "s" is the side, one side is x - 6.