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If the area of a square is doubled, the ratio of the new side to the original side is:
- a)2 : 1
- b)√2 : 1
- c)1 : √2
- d)4 : 1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the area of a square is doubled, the ratio of the new side to the o...
Let the original side be a. Then the original area = a2.
New area = 2a2, so new side = √(2a2) = a√2.
Ratio of new side to original side = a√2 : a = √2 : 1.
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If the area of a square is doubled, the ratio of the new side to the o...
Understanding the Problem
When the area of a square is doubled, we need to find the ratio of the new side length to the original side length.
Original Area and Side Length
- Let the original side length of the square be 's'.
- The area of the square is given by the formula: Area = side × side = s².
New Area
- If the area of the square is doubled, the new area becomes:
New Area = 2 × s².
Finding the New Side Length
- To find the new side length, we need to set up the equation:
New Area = new side × new side = new side².
- Therefore, we have:
new side² = 2 × s².
Calculating the New Side Length
- Taking the square root of both sides gives us:
new side = √(2 × s²) = s × √2.
Finding the Ratio
- Now, we can find the ratio of the new side to the original side:
Ratio = new side / original side = (s × √2) / s = √2.
Conclusion
- Thus, the ratio of the new side to the original side is √2 : 1.
- Therefore, the correct answer is option 'B'.
When the area of a square is doubled, we need to find the ratio of the new side length to the original side length.
Original Area and Side Length
- Let the original side length of the square be 's'.
- The area of the square is given by the formula: Area = side × side = s².
New Area
- If the area of the square is doubled, the new area becomes:
New Area = 2 × s².
Finding the New Side Length
- To find the new side length, we need to set up the equation:
New Area = new side × new side = new side².
- Therefore, we have:
new side² = 2 × s².
Calculating the New Side Length
- Taking the square root of both sides gives us:
new side = √(2 × s²) = s × √2.
Finding the Ratio
- Now, we can find the ratio of the new side to the original side:
Ratio = new side / original side = (s × √2) / s = √2.
Conclusion
- Thus, the ratio of the new side to the original side is √2 : 1.
- Therefore, the correct answer is option 'B'.
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