Correct option is (d) 3 : 4
Let the length and breadth of the rectangle be L and B, respectively.
Then, Diagonal = \(\sqrt{L^2 + B^2}\)
Given, L + B − \(\sqrt{L^2 + B^2} = \frac 12 L\)
⇒ \(\sqrt{L^2 + B^2} = L - \frac 12 L + B \)
\( = \frac 12 L + B\)
Squaring both the sides,
\(L^2 + B^2 = \left(\frac L2 + B\right)^2\)
⇒ \(L^2 + B^2 = \frac{L^2}4 + B^2 + LB\)
⇒ \(\frac{3L^2}4 = LB\)
⇒ \(\frac{LB}{L^2} = \frac 34\)
⇒ \(\frac BL = \frac 34\)