Rectangle — If both sides are increased by 5%, by what percentage does the diagonal increase?

Introduction / Context:
Scaling every linear dimension of a rectangle by the same factor scales the diagonal by the same factor because the shape is similar. The diagonal is a linear measure, not an area.

Given Data / Assumptions:

• Sides scale by 1.05 each.
• Diagonal d = sqrt(L^2 + B^2).

Concept / Approach:
New diagonal d' = sqrt((1.05L)^2 + (1.05B)^2) = 1.05 * sqrt(L^2 + B^2) = 1.05 * d. Hence percentage increase equals 5%.

Step-by-Step Solution:
Scale factor for diagonal = 1.05 ⇒ increase = (1.05 − 1) * 100% = 5%

Verification / Alternative check:
Pick L = 3, B = 4 ⇒ d = 5. After scaling by 1.05: d' = 5 * 1.05 = 5.25, which is 5% more.

Why Other Options Are Wrong:
4% or 6% come from confusing area vs length scaling; 9% would be the area-like change; 10% is arbitrary.

Common Pitfalls:
Applying area-percentage logic to a length measure; area would increase by about 10.25% (1.05^2 − 1).

Final Answer:
5%