A rectangle has diagonal √41 cm and area 20 cm². What is its perimeter?

Problem restatementGiven diagonal d and area A of a rectangle with sides a and b, find the perimeter 2(a + b).

Given data

• a² + b² = d² = 41
• ab = 20

Concept/ApproachUse (a + b)² = a² + b² + 2ab to find a + b directly without solving for a and b separately.

Step-by-Step calculation(a + b)² = 41 + 2(20) = 81a + b = 9Perimeter = 2(a + b) = 18 cm

Verification/AlternativeIf a and b are roots of t² − 9t + 20 = 0 ⇒ (t − 4)(t − 5) = 0 ⇒ sides 4 and 5 cm. Perimeter = 2(4 + 5) = 18 cm.

Common pitfallsAttempting to use Pythagoras directly to find one side without leveraging the area; the symmetric identity is faster.

Final Answer18 cm