One side of a square is increased by 35%. By what percentage must the other side be reduced so that the area remains the same?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(25\frac{25}{27}\%\)
Area \(=\) side \(\times\) side. To keep the product the same, the other side must fall in the opposite ratio, and the fall is measured on its old value.
Take each side as 100; one side becomes 135
Other side \(x\): \(135\times x=100\times100\), so \(\displaystyle x=\frac{10000}{135}=\frac{2000}{27}\)
Reduction \(\displaystyle =100-\frac{2000}{27}=\frac{700}{27}=25\frac{25}{27}\%\)
The other side must be reduced by \(25\frac{25}{27}\%\).