A rectangle has a length L and a width W, where L > W. If the width, W, is increased by 10%, which one of the following statements is correct for all values of L and W?
Answer
(C)
Explanation
The new width is \(1.1W\), while the length stays \(L\).
- Area: \(L \times 1.1W = 1.1LW\), exactly 10% more for every \(L\) and \(W\).
- Perimeter: it grows by \(0.2W\), which is less than 10% of \(2(L + W)\) because the length does not grow.
- Diagonal: \(\sqrt{L^{2} + 1.21W^{2}} \lt 1.1\sqrt{L^{2} + W^{2}}\), so it also grows by less than 10%.
- Square: only if \(1.1W = L\), which holds for one particular ratio, not for all values.
Answer: C