Rectangle — If both sides are increased by 10%, by what percentage does the diagonal increase?

Introduction / Context:As with any uniform linear scaling, the diagonal scales by the same linear factor because it depends linearly on the sides under the square-root relation.

Given Data / Assumptions:

• Sides scale by 1.10 each.

Concept / Approach:d' = sqrt((1.10L)^2 + (1.10B)^2) = 1.10 * sqrt(L^2 + B^2) = 1.10 * d ⇒ 10% increase.

Step-by-Step Solution:Increase = (1.10 − 1) * 100% = 10%

Verification / Alternative check:Example L = 6, B = 8: d = 10 ⇒ new d = 11 ⇒ exactly +10%.

Why Other Options Are Wrong:15%, 18%, 20% are not applicable to a length; they reflect area-like compounding or guesses.

Common Pitfalls:Confusing area change (which would be 21%) with diagonal change (10%).

Final Answer:10%