Correct Answer - Option 2 : 6%
Formula used:
Diagonal of a rectangle = \(\sqrt{l^2 + b^2}\)
Calculation:
Let the length and breath be 'l' and 'b'
After increase of 6%,
Length = l + 6l/100
⇒ 106l/100 = 53l/50
After increase of 6%,
Breath = b = 53b/50
Diagonal of a rectangle = \(\sqrt{l^2 + b^2}\)
After increase 6% diagnals = \(\sqrt{(53l/50)^2 + (53b/50)^2}\)
⇒ \(\sqrt{(53/50)^2(l^2 + b^2)}\) = \((53/50)^2\sqrt{l^2 + b^2}\)
The length of diagonals originally = \(\sqrt{l^2 + b^2}\)
Percentage increase in diagonals =( \(\sqrt{(53/50)^2(l^2 + b^2)}\)/\(\sqrt{l^2 + b^2}\))× 100
⇒ 53/50((\(\sqrt{l^2+ b^2}-\sqrt{l^2 - b^2}\))/\(\sqrt{l^2 + b^2}\)) ×100
⇒Required percentage change = [(53/50) - 1] × 100 = 6%
∴ Required percentage change is 6%