The whole surface area of a rectangular block is 8788 sq cm and its dimensions are in the ratio 4 : 3 : 2 (length : breadth : height). Find the length (in cm).

Introduction / Context:
When only the surface area and the ratio of edges are given, introduce a common factor x to express the three dimensions and substitute into the surface-area formula. Solve for x, then recover each dimension as a multiple of x. This is a common technique for ratio-based solids questions.

Given Data / Assumptions:

• Ratios: l : b : h = 4 : 3 : 2 ⇒ l = 4x, b = 3x, h = 2x.
• Total surface area S = 8788 cm^2.
• Formula: S = 2(lb + bh + hl).

Concept / Approach:
Compute lb, bh, hl in terms of x, sum, multiply by 2, set equal to 8788, and solve x. Then find l = 4x.

Step-by-Step Solution:
lb = (4x)(3x) = 12x^2bh = (3x)(2x) = 6x^2hl = (2x)(4x) = 8x^2S = 2(12 + 6 + 8)x^2 = 2 * 26x^2 = 52x^252x^2 = 8788 ⇒ x^2 = 169 ⇒ x = 13Length l = 4x = 4 * 13 = 52 cm

Verification / Alternative check:
Compute b = 39 cm and h = 26 cm from x = 13; recomputing S gives 8788 cm^2, confirming consistency.

Why Other Options Are Wrong:
26 and 13 are smaller multiples (h and x); 104 cm doubles l mistakenly.

Common Pitfalls:
Dropping the factor 2 in S; mishandling squared ratios; misadding 12 + 6 + 8.

Final Answer:
52 cm