GATE CE 2025 Set 2 — Question 10
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumMensuration & GeometryQuantitative AptitudeGeneral Aptitude
General Aptitude → Quantitative Aptitude → Mensuration & Geometry
Last updated
Question
Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?Note: The figure shown is representative.
Correct answer
(C) 12.0
Solution
The minimum distance from village P to the straight road QR is the length of the altitude from P to the side QR in . Let the sides be km, km, and km.First, calculate the area of using Heron's formula:
Semi-perimeter km.
Area .The area is also given by :
.
km.Thus, the minimum length of the connecting road is 12.0 km.
Semi-perimeter km.
Area .The area is also given by :
.
km.Thus, the minimum length of the connecting road is 12.0 km.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Quantitative Aptitude
2026 Set 2 Q1'The team ____ more than 300 runs in 20 overs ____ rains. However, some players needed to…2026 Set 1 Q1‘The shopkeeper sells lemons.’ In this sentence, the word ‘lemons’ is the ________.2026 Set 2 Q2If a positive real satisfies the following equation then…2026 Set 1 Q2The figure below is supposed to show three non-overlapping shapes – one oval and two triangles.…2026 Set 2 Q3The next figure (indicated by ‘?’) in the sequence is