Rectangle with given perimeter and offset length The length of a rectangle is 10 cm more than its breadth. If the perimeter is 44 cm, find the length of the diagonal (in cm).

Introduction / Context:This problem blends linear relations (perimeter and difference between sides) with the Pythagorean theorem to determine the rectangle’s diagonal.

Given Data / Assumptions:

• Perimeter P = 44 cm
• Let breadth = b; length = b + 10
• Diagonal d = sqrt(l^2 + b^2)

Concept / Approach:Perimeter relation: 2(l + b) = 44 ⇒ l + b = 22. Combined with l = b + 10 gives a solvable linear pair for l and b. Then apply Pythagoras for the diagonal.

Step-by-Step Solution:

Verification / Alternative check:Perimeter check: 2(16 + 6) = 44 (correct). The diagonal magnitude is reasonable for these sides.

Why Other Options Are Wrong:12.50 cm, 14.21 cm, and 15.98 cm are not the true space diagonal for sides 16 cm and 6 cm.

Common Pitfalls:Mixing up perimeter with area or mistakenly using (l - b) instead of (l + b) to form equations will lead to incorrect side values.

Final Answer:17.08 cm