9514 1404 393
Answer:
x = ±10 m
Step-by-step explanation:
For a square of side length x, the area is given by ...
A = x²
Your square has an area of A=100, so the equation can be written ...
100 = x²
Subtracting 100 from both sides gives ...
x² -100 = 0
and factoring that yields ...
(x -10)(x +10) = 0
The zero product rule tells us that a product is only zero if one or more factors is zero. The values of x that make these factors zero are ...
(x -10) = 0 ⇒ x = 10
(x +10) = 0 ⇒ x = -10
Each side of the square measures 10 meters.
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There are two possible solutions because the square of a negative number is positive, as is the square of a positive number. (-10)² = 100, just as 10² = 100. There is nothing in the equation that restricts x to positive values.
However, since x is a length equal to the side length of a real geometric object, it cannot have a negative value. So, the only viable answer is x = 10 meters. The solution x = -10 meters is considered to be "extraneous," an artifact of the solution process for the equation.
