In a square, if the length of one side is doubled, what happens to the area of t

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Question: In a square, if the length of one side is doubled, what happens to the area of the square?

Options:

Correct Answer: It quadruples

Solution:

If the side length of a square is doubled, the area increases by a factor of four (since area = side^2).

In a square, if the length of one side is doubled, what happens to the area of the square?

In a square, if the length of one side is doubled, what happens to the area of the square?

Step 1: Understand that a square has four equal sides.
Step 2: Let the original length of one side of the square be 's'.
Step 3: Calculate the area of the original square using the formula: Area = side^2. So, Area = s^2.
Step 4: Now, if we double the length of one side, the new length becomes '2s'.
Step 5: Calculate the area of the new square using the same formula: Area = (new side)^2. So, Area = (2s)^2.
Step 6: Simplify (2s)^2 to get 4s^2.
Step 7: Compare the new area (4s^2) to the original area (s^2).
Step 8: Notice that 4s^2 is four times the original area (s^2).
Step 9: Conclude that when the side length is doubled, the area increases by a factor of four.

Area of a Square – The area of a square is calculated by squaring the length of one of its sides (Area = side^2).
Effect of Doubling Dimensions – Doubling the length of a side results in the area increasing by a factor of four, as (2 * side)^2 = 4 * (side^2).