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In a square, if the length of one side is doubled, what happens to the area of t
In a square, if the length of one side is doubled, what happens to the area of the square?
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In a square, if the length of one side is doubled, what happens to the area of the square?
It remains the same
It doubles
It quadruples
It increases by 50%
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If the side length of a square is doubled, the area increases by a factor of four (since area = side^2).
Questions & Step-by-step Solutions
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Q
Q: In a square, if the length of one side is doubled, what happens to the area of the square?
Solution:
If the side length of a square is doubled, the area increases by a factor of four (since area = side^2).
Steps: 9
Show Steps
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.
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