A rectangle has a length L and a width W, where L W. The width W is increased by 10% for all values of L and W. Which ...

Question

A rectangle has a length L and a width W, where L > W. The width W is increased by 10% for all values of L and W. Which one of the following statements is correct?

A. Perimeter increases by 10%.
B. Length of the diagonals increases by 10%.
C. Area increases by 10%.
D. The rectangle becomes a square.

Accepted Answer

When W is increased by 10%, the area increases by exactly 10% for all values of L and W (option C). When the width W is replaced by 1.1W while L stays the same, we can recompute each quantity and see what changes. The area goes from L*W to L*(1.1W) = 1.1LW, which is exactly a 10% increase. The perimeter changes from 2(L+W) to 2(L+1.1W), which is 2L+2.2W — the increase is 0.2W, but this is not 10% of 2(L+W) unless W=L. The diagonal changes from sqrt(L^2+W^2) to sqrt(L^2+1.21W^2), which is not a simple 10% increase. The rectangle becomes a square only when L=W, but we are told L>W.