(b) 5 : 3.
By physically folding the square sheet of paper as per the conditions stated in the question, we can see that EF is the crease along which the fold is made. Also,
MF = FB and MB ⊥ EF.
We need to find BF : FC.
Let each side of the square be a units and CF = x units
Then, BF = (a – x) units and MF = (a – x) units.
In ΔMFC, MF2 = MC2 + FC2
⇒ FB2 = MC2 + FC2 (Since MF = FB)
⇒ (a – x)2 = (a/2)2 + x2
⇒ a2 + x2 – 2ax = \(\frac{a^2}{4}\) + x2
⇒ 2ax = a2 - \(\frac{a^2}{4}\) = \(\frac{3a^2}{4}\)
⇒ x = \(\frac{3a}{8}\) ⇒ a - x = a - \(\frac{3a}{8}\) = \(\frac{5a}{8}\)
∴ BF : FC = (x - a) : x
= \(\frac{5a}{8}\) : \(\frac{3a}{8}\) = 5 : 3.