Final answer:
The length of AB is 3 cm.
Step-by-step explanation:
Given that QR = 10 cm and BC = PQ, we can conclude that PQ = 10 cm as well. The perimeter of ABCD is 26 cm, so the sum of the lengths of all four sides of the rectangle is 26 cm. Let's assume that the length of AB is x cm. This means that the length of BC is also x cm, and the length of CD is 10 cm. Adding these lengths together, we get:
10 + x + 10 + x = 26 cm
Simplifying the equation:
2x + 20 = 26 cm
Subtracting 20 from both sides of the equation:
2x = 6 cm
Dividing both sides of the equation by 2:
x = 3 cm
Therefore, the length of AB is 3 cm.