In the given figure, ABCD is a rectangle. As per the given information, the length of PQ is :

1. 12 cm

2. 14 cm

3. 20 cm

4. 10 cm

From figure,

AP = PB and BQ = QC.

∴ P is the mid-point of AB and Q is the mid-point of BC.

In △ ADC,

⇒ AD² + CD² = AC² (By pythagoras theorem)

⇒ 12² + 16² = AC²

⇒ 144 + 256 = AC²

⇒ AC² = 400

⇒ AC = $\sqrt{400}$ = 20 cm.

By mid-point theorem,

The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.

∴ PQ = $\dfrac{1}{2} AC = \dfrac{1}{2} \times 20$ = 10 cm.

Hence, Option 4 is the correct option.