Rectangle transformation: The length of a rectangle is twice its breadth. If length is decreased by 5 cm and breadth is increased by 5 cm, the area increases by 75 sq cm. Find the original length of the rectangle.

Introduction / Context:
This algebra problem involves relating original dimensions to changed dimensions and comparing areas to find unknowns.

Given Data / Assumptions:

• L = 2B (original)
• (L - 5) * (B + 5) = L * B + 75
• All lengths in cm; rectangle properties standard.

Concept / Approach:
Expand the changed-area expression, simplify, and use L = 2B to solve a linear system for B and L.

Step-by-Step Solution:

Verification / Alternative check:
Original area LB = 40*20 = 800. New area (35*25) = 875. Increase = 75 sq cm, matches the condition.

Why Other Options Are Wrong:
10cm, 20cm, 30cm, 35cm do not satisfy both L = 2B and L - B = 20 simultaneously.

Common Pitfalls:
Dropping terms during expansion or mixing the sign in L - B; also, assuming both changes are equal but forgetting L = 2B.

Final Answer:
40cm