Discussion

Explanation:

Let the longer side of the rectangle is 2a and the shorter side is b as shown in the figure.

Using pythagoras theorem, we get
a² + b² = 2² = 4   ...(1)

Also, AM ≥ GM
⇒ $\frac{{\mathrm{a}}^2+{\mathrm{b}}^2}{2}$ ≥ $\sqrt{{\mathrm{a}}^2{\mathrm{b}}^2}$

⇒ a² + b² ≥ 2ab

⇒ 4 ≥ 2ab

⇒ 2 ≥ ab

∴ Highest value of ab = 2, when a = b.

⇒ Ratio of longer side to shorter side = 2a : b = 2 : 1.

Hence, option (a).

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