Question-5

A rectangle has length \(L\) and 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 \(W\)?

• Perimeter increases by \(10\%\).
• Length of the diagonals increases by \(10\%\).
• Area increases by \(10\%\).
• The rectangle becomes a square

NoteAnswer

• Perimeter increases by \(10\%\).
• Length of the diagonals increases by \(10\%\).
• Area increases by \(10\%\).
• The rectangle becomes a square

TipSolution

We see that the percentage change in area is:

\[ \frac{1.1LW-LW}{LW} \times 100=10\% \]

This is independent of \(L\) and \(W\).