Cuboid from sum of edges and diagonal (rephrased) — compute surface area: The sum of the length, breadth, and height of a cuboid is 19 cm, and its space diagonal is 5√5 cm. What is the total surface area of the cuboid?

Introduction / Context:Same setup as a classic identity problem: with l + b + h and the space diagonal known, compute the pairwise products and hence the total surface area.

Given Data / Assumptions:

• l + b + h = 19 cm
• d = 5√5 cm ⇒ d^2 = 125
• Surface area S = 2(lb + bh + hl)

Concept / Approach:Use (l + b + h)^2 = d^2 + 2(lb + bh + hl). Rearranging gives the sum of pairwise products directly.

Step-by-Step Solution:(l + b + h)^2 − d^2 = 361 − 125 = 2362(lb + bh + hl) = 236 ⇒ S = 236 cm2

Verification / Alternative check:Dimensions need not be individually determined; identity-based computation is sufficient.

Why Other Options Are Wrong:361 and 125 are intermediate squares; “None” is unnecessary once identity is applied.

Common Pitfalls:Forgetting to take 2 into account or mis-squaring 19.

Final Answer:236 cm2