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What is the value of the variable \( x \) if the perimeter of the patio is exactly 200 feet?

A) \( x = 25 \)
B) \( x = 50 \)
C) \( x = 75 \)
D) \( x = 100 \)

Answer :

Final answer:

The question involves calculating the sides of a square patio with a perimeter of 200 feet. Assuming each side of the square is represented as x, to find x you divide the total perimeter (200 feet) by 4 (for the four sides of the square), which results in 50 feet per side (option B).

Explanation:

The question pertains to the concept of perimeter as applied to a rectangular patio. If the perimeter of the patio is 200 feet, this means that the sum of all the sides of the rectangle (2x on the length plus 2x on the width) equals 200 feet.

If we consider a square patio, where every side is equal, we could state 4x = 200 (because a square has four sides of equal lengths). From here, we can isolate the x-value by dividing both sides of the equation by 4. That would yield x = 200 / 4 = 50

Therefore, the answer is option B, x = 50

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