In a rectangle, the ratio of perimeter to breadth is 5:1 and the area is 216 cm². What is its length?

Problem restatementGiven P : B = 5 : 1 and area, determine the rectangle's length.

Given data

• Perimeter P : breadth B = 5 : 1 ⇒ Let B = x, P = 5x
• Perimeter P = 2(L + B)
• Area = L × B = 216

Concept/ApproachUse P = 2(L + B) to link L and x; substitute B = x into area to solve for x and then L.

Step-by-Step calculation2(L + x) = 5x ⇒ L + x = 2.5x ⇒ L = 1.5xArea: L × B = 1.5x × x = 1.5x² = 216x² = 216 / 1.5 = 144 ⇒ x = 12 cm (breadth)Length L = 1.5 × 12 = 18 cm

Verification/AlternativePerimeter = 2(18 + 12) = 60; P:B = 60:12 = 5:1 as required.

Common pitfallsTaking the 5:1 as L:B instead of P:B.

Final Answer18 cm