Rectangle from area and perimeter:\nA rectangle has area 60 cm² and perimeter 34 cm. Find the length of its diagonal (in cm).

Introduction / Context:
With area and perimeter given, one can find the sum and product of the sides, which allows recovery of the diagonal using the identity a^2 + b^2 = (a + b)^2 − 2ab. The diagonal is then √(a^2 + b^2).

Given Data / Assumptions:

• Area ab = 60.
• Perimeter 2(a + b) = 34 ⇒ a + b = 17.

Concept / Approach:
Compute a^2 + b^2 from the sum and product. Then diagonal d = √(a^2 + b^2). No need to solve for a and b individually.

Step-by-Step Solution:

Verification / Alternative check:
One possible pair is a = 12, b = 5 (since 12 + 5 = 17 and 12*5 = 60). Diagonal = √(12^2 + 5^2) = √169 = 13, confirming.

Why Other Options Are Wrong:
11 and 15 do not satisfy the derived Pythagorean relation given the constraints.

Common Pitfalls:
Trying to factor 60 first—unnecessary; use identities directly.

Final Answer:
13 cm