Discussion
Given below are two statements:
Statement I : If the side of a square is doubled, its area also doubles.
Statement II : The perimeter of a square increases linearly with the length of its side.
In the light of the above statements,choose the Correct answer from the options given below:
Answer: D
Statement I is false but Statement II is true.
Area grows with the square of the side. Doubling a side of length a gives
\[ (2a)^2 = 4a^2 \]
so the area becomes four times as large, not twice. Statement I is false.
The perimeter is \(4a\), a straight-line (linear) function of a: doubling the side doubles the perimeter. Statement II is true. The options calling Statement I true confuse the perimeter's behaviour with the area's.
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