Trapezium from area and difference: The difference between the two parallel sides of a trapezium is 4 cm, the perpendicular distance is 19 cm, and the area is 475 sq cm. Find the lengths of the parallel sides.

Introduction / Context:
Solving a trapezium from area and difference of bases involves forming and solving simultaneous linear equations.

Given Data / Assumptions:

• Let bases be a and b with a > b
• a - b = 4 cm
• h = 19 cm
• Area A = 475 sq cm

Concept / Approach:
Area formula: A = (1/2)(a + b)h. Use A and h to get (a + b), then combine with (a - b) to solve a and b.

Step-by-Step Solution:

Verification / Alternative check:
Area check: (1/2)*(27+23)*19 = (1/2)*50*19 = 475. Difference 27 - 23 = 4. Consistent.

Why Other Options Are Wrong:
Other pairs do not satisfy both the sum 50 and difference 4 simultaneously.

Common Pitfalls:
Mixing which base is larger or miscomputing 950/19 (ensure exact division to 50).

Final Answer:
27 and 23