Rectangle — Given Ratio of Length to Perimeter 5 : 18: If L : P = 5 : 18 for a rectangle, what is the ratio L : B?

Introduction / Context:
Relating a rectangle’s length directly to its perimeter allows back-solving for the breadth via P = 2(L + B). Converting the L : P ratio into an equation yields the desired L : B ratio without needing actual numbers.

Given Data / Assumptions:

• L : P = 5 : 18 ⇒ P = (18/5)L
• Perimeter formula: P = 2(L + B)

Concept / Approach:
Set 2(L + B) = (18/5)L, solve for B in terms of L, then express L : B in simplest integer form by clearing denominators.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 4 : 3 and 3 : 5 do not satisfy P = (18/5)L.
• 4 : 7 and 7 : 4 invert or distort the derived proportion.

Common Pitfalls:

• Forgetting that perimeter is twice the semiperimeter leading to a factor-of-two error.

Final Answer:
5 : 4.