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Answer the following questions by selecting the most appropriate option.
Q. If two adjacent sides of a square paper are decreased by 20% and 40% respectively, by what percentage does the new area decrease?
- a)48%
- b)50%
- c)52%
- d)60%
Correct answer is option 'C'. Can you explain this answer?
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Understanding the Problem
To solve the problem, we need to determine the percentage decrease in the area of a square paper when its adjacent sides are reduced by specific percentages.
Initial Area Calculation
- Let the original side length of the square be \( s \).
- The area \( A \) of the square is given by:
\[ A = s^2 \]
New Side Lengths After Decrease
- The first side is decreased by 20%, so the new length is:
\[ s_1 = s - 0.20s = 0.80s \]
- The second side is decreased by 40%, so the new length is:
\[ s_2 = s - 0.40s = 0.60s \]
New Area Calculation
- The new area \( A' \) with the reduced sides is:
\[ A' = s_1 \times s_2 = (0.80s) \times (0.60s) \]
- Simplifying this gives:
\[ A' = 0.48s^2 \]
Percentage Decrease in Area
- The decrease in area can be calculated as follows:
\[ \text{Decrease} = A - A' = s^2 - 0.48s^2 = 0.52s^2 \]
- To find the percentage decrease:
\[ \text{Percentage Decrease} = \left( \frac{\text{Decrease}}{A} \right) \times 100 = \left( \frac{0.52s^2}{s^2} \right) \times 100 \]
\[ \text{Percentage Decrease} = 52\% \]
Conclusion
Thus, the area of the square paper decreases by **52%** when the two adjacent sides are decreased by 20% and 40% respectively. Therefore, the correct answer is option 'C'.
To solve the problem, we need to determine the percentage decrease in the area of a square paper when its adjacent sides are reduced by specific percentages.
Initial Area Calculation
- Let the original side length of the square be \( s \).
- The area \( A \) of the square is given by:
\[ A = s^2 \]
New Side Lengths After Decrease
- The first side is decreased by 20%, so the new length is:
\[ s_1 = s - 0.20s = 0.80s \]
- The second side is decreased by 40%, so the new length is:
\[ s_2 = s - 0.40s = 0.60s \]
New Area Calculation
- The new area \( A' \) with the reduced sides is:
\[ A' = s_1 \times s_2 = (0.80s) \times (0.60s) \]
- Simplifying this gives:
\[ A' = 0.48s^2 \]
Percentage Decrease in Area
- The decrease in area can be calculated as follows:
\[ \text{Decrease} = A - A' = s^2 - 0.48s^2 = 0.52s^2 \]
- To find the percentage decrease:
\[ \text{Percentage Decrease} = \left( \frac{\text{Decrease}}{A} \right) \times 100 = \left( \frac{0.52s^2}{s^2} \right) \times 100 \]
\[ \text{Percentage Decrease} = 52\% \]
Conclusion
Thus, the area of the square paper decreases by **52%** when the two adjacent sides are decreased by 20% and 40% respectively. Therefore, the correct answer is option 'C'.
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Answer the following questions by selecting the most appropriate option.Q. If two adjacent sides of a square paper are decreased by 20% and 40% respectively, by what percentage does the new area decrease?a)48%b)50%c)52%d)60%Correct answer is option 'C'. Can you explain this answer?
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