One side of a rectangle is increased by 25%. By what percentage must the other side be reduced so that the area remains the same?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 20%
Area \(=\) length \(\times\) breadth. Take both sides as 100; the new breadth must bring the product back to the same area.
New length \(=100+25=125\)
Breadth needed \(\displaystyle =\frac{100\times100}{125}=80\)
Reduction \(=100-80=20\), that is 20%
The other side must be reduced by 20%.
Why the other options are incorrect
Option (1) 12.5% — Incorrect. This halves the increase; the product of the two factors must be 1.
Option (2) \(33\frac{1}{3}\%\) — Incorrect. This is the change needed when the first side is reduced; here it is increased.
Option (3) 25% — Incorrect. Reducing the other side by 25% leaves the area at \(1.25\times0.75=0.9375\) of the old area, not the same.