GATE ECE 2025 | GA | Question: 7

Question

A stick of length one meter is broken at two locations at distances of $b_{1}$ and $b_{2}$ from the origin $(0)$, as shown in the figure. Note that $0 < b_{1} < b_{2}<1$. Which one of the following is NOT a necessary condition for forming a triangle using the three pieces?

Note: All lengths are in meter. The figure shown is representative.

• A. $b_{1}<0.5$
• B. $b_{2}>0.5$
• C. $b_{2} < b_{1} + 0.5$
• D. $b_{1}+b_{2}<1$

Answer 1

For triangle:

Largest piece < sum of other two
Since total length = 1, condition becomes:

Largest piece < 1/2

So all three must be < 0.5

1. b₁ < 0.5 

2. b₂ − b₁ < 0.5 → b₂ < b₁ + 0.5

3. 1 − b₂ < 0.5 → b₂ > 0.5 

b₁ + b₂ < 1    -> This is NOT required for triangle condition.

So answer = D. b₁ + b₂ < 1