Area of two adjacent walls (no doors/windows) — which statements suffice? I. Floor area (L * B) of the hall is 24 m^2. II. Breadth : Length : Height = 4 : 6 : 5. III. Area of one wall is 30 m^2.
Correct Answer: Only I and II
Introduction / Context:The original wording asked for “cost” but no painting rate was provided. Under the Recovery-First Policy, we minimally repair the stem to ask for the area of two adjacent walls (sum of areas), which is uniquely determinable from geometric data alone.
Given Data / Assumptions:
- I: Floor area L * B = 24 m^2.
- II: B : L : H = 4 : 6 : 5 ⇒ Let (B, L, H) = (4k, 6k, 5k).
- III: Area of one wall (unspecified which) = 30 m^2.
Concept / Approach:Area of two adjacent walls = L * H + B * H = H * (L + B). Using I and II, the scale k can be solved, yielding exact dimensions and therefore the desired area.
Step-by-Step Solution:
From II, set B = 4k, L = 6k, H = 5k.From I: L * B = (6k)*(4k) = 24k^2 = 24 ⇒ k = 1 m.Thus B = 4 m, L = 6 m, H = 5 m.Sum of adjacent wall areas = L*H + B*H = 6*5 + 4*5 = 50 m^2.Verification / Alternative check:Statement III alone gives only one wall’s area and does not determine the other without additional dimensions.
Why Other Options Are Wrong:
- Only II: Lacks scale; k is unknown.
- Only III: Insufficient to deduce the second wall’s area.
- Either I or III: Neither alone suffices.
- Only I and III: Still missing H or the other dimension to fully determine the second wall.
Common Pitfalls:Assuming floor area alone fixes height; it does not without proportions.
Final Answer:Only I and II