The greatest length of the scale that can measure exactly 20 cm, 90 cm, 1 m 25 cm and 1 m 30 cm length is:

5 cm 

Convert all lengths to centimeters:

• 20 cm = 20 cm
• 90 cm = 90 cm
• 1 m 25 cm = 125 cm
• 1 m 30 cm = 130 cm

We need the greatest length of the scale, i.e., the HCF (GCD) of 20, 90, 125, and 130.

$20 = 2^2 \times 5$

$90 = 2 \times 3^2 \times 5$

$125 = 5^3$

$130 = 2 \times 5 \times 13$

The only common factor is 5.

Therefore, HCF = 5 cm