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If the length of a rectangle is increased by 80%, what would be the percentage decrease (correct to one place of decimal) in the
width to maintain the same area?
44.4%
42.5%
40.2%
43.5%
- The area of a rectangle is given by the formula \( \text{Area} = \text{Length} \times \text{Width} \).
- If the length is increased by 80%, the new length becomes \( 1.8 \times \text{Original Length} \).
- To maintain the same area, the width must decrease to counteract the increased length.
- Let \( x \) be the factor by which the width should decrease.
- Then the new width is \( \text{Original Width} \times x \).
- Equating the areas: \( \text{Original Length} \times \text{Original Width} = 1.8 \times \text{Original Length} \times \text{Original Width} \times x \).
- Cancel out common terms and solve for \( x \): \( 1 = 1.8x \); thus, \( x = \frac{1}{1.8} \approx 0.5556 \).
- This is a 44.4% decrease in width: \( (1 - 0.5556) \times 100 \approx 44.4 \%\).
- Correct Answer: Option 1 - 44.4%
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By: santosh ProfileResourcesReport error
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