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

Introduction / Context:
This question combines rectangle perimeter with the Pythagoras theorem for the diagonal. First, perimeter gives a relationship between length and breadth: P = 2*(L + B). With the extra information that L is 10 cm more than B, we can solve for both sides exactly. Then the diagonal is the hypotenuse of a right triangle whose legs are L and B, so diagonal d = sqrt(L^2 + B^2). The only approximation happens at the final square root, which is why the answer is given to two decimal places.

Given Data / Assumptions:

• Length L = B + 10 cm
• Perimeter P = 44 cm
• Perimeter formula: 2*(L + B) = 44
• Diagonal formula: d = sqrt(L^2 + B^2)

Concept / Approach:
Use perimeter to solve for L and B, then use Pythagoras to compute the diagonal. Keep units in cm throughout.

Step-by-Step Solution:
2*(L + B) = 44 => L + B = 22 L = B + 10 Substitute: (B + 10) + B = 22 => 2B = 12 => B = 6 cm L = 6 + 10 = 16 cm Diagonal d = sqrt(16^2 + 6^2) = sqrt(256 + 36) = sqrt(292) sqrt(292) ≈ 17.08 cm

Verification / Alternative check:
Check perimeter: 2*(16+6)=2*22=44 cm, correct. Since diagonal must be longer than the longer side 16 cm and shorter than 16+6=22 cm, 17.08 cm is a reasonable value in the correct range.

Why Other Options Are Wrong:
12.50 and 14.21 are too small (even smaller than the length 16 cm in some cases). 15.98 comes from using wrong sides or rounding errors. 16.00 would imply a square-like diagonal and does not fit L=16, B=6.

Common Pitfalls:
Forgetting to divide perimeter by 2, mixing up which side is 10 cm longer, or adding squares incorrectly before taking square root.

Final Answer:
The diagonal of the rectangle is approximately 17.08 cm.