Rectangle from area and perimeter — find the diagonal: A rectangular carpet has an area of 120 sq m and a perimeter of 46 m. Determine the length of its diagonal (in meters).

Introduction / Context:
This problem combines two standard rectangle formulas—area and perimeter—to recover the side lengths and then uses the Pythagoras relation to get the diagonal. These are core skills for geometry aptitude questions.

Given Data / Assumptions:

• Area = 120 sq m
• Perimeter = 46 m → sum of adjacent sides l + w = 23
• Rectangle right angle allows diagonal via l^2 + w^2

Concept / Approach:
If l + w = 23 and l * w = 120, then l and w are the roots of t^2 − 23t + 120 = 0. After finding l and w, compute diagonal d using d^2 = l^2 + w^2.

Step-by-Step Solution:
Quadratic: t^2 − 23t + 120 = 0Discriminant = 23^2 − 4*120 = 529 − 480 = 49Roots: (23 ± 7)/2 → 15 and 8 → (l, w) = (15, 8)Diagonal d = sqrt(15^2 + 8^2) = sqrt(225 + 64) = sqrt(289) = 17 m

Verification / Alternative check:
Perimeter: 2*(15 + 8) = 46 ✓; Area: 15*8 = 120 ✓; Pythagorean triple (8, 15, 17) confirms.

Why Other Options Are Wrong:
15 m and 16 m are smaller than the longer side; 20 m exceeds required hypotenuse length for these sides.

Common Pitfalls:
Using 23^2 = l^2 + w^2 by mistake; Pythagoras applies to sides, not their sum.

Final Answer:
17 m