In a triangle ABC, D and E are points on sides AB and AC respectively such that DE ∥ BC. If AD = x, DB = x − 2, AE = x + 2 and EC = x − 1, find the value of x.
एक त्रिभुज (Triangle) ABC में, D और E क्रमशः भुजाओं (Side) AB और AC पर ऐसे बिंदु (Point) हैं कि DE ∥ BC है। यदि AD = x, DB = x − 2, AE = x + 2 और EC = x − 1 है, तो x का मान ज्ञात कीजिए।
Answer और ExplanationAnswer and explanation
Answer: (A) 4
DE ∥ BC है, इसलिए आधारभूत समानुपातिकता प्रमेय (BPT) से:
ADDB = AEEC ⇒ xx − 2 = x + 2x − 1
x(x − 1) = (x + 2)(x − 2)
x² − x = x² − 4 ⇒ x = 4
जाँच: DB = 2, EC = 3 (दोनों धनात्मक) और 42 = 63 ✓
✓
x = 4।
DE ∥ BC, so by the basic proportionality theorem (BPT):
ADDB = AEEC ⇒ xx − 2 = x + 2x − 1
x(x − 1) = (x + 2)(x − 2)
x² − x = x² − 4 ⇒ x = 4
Check: DB = 2, EC = 3 (both positive) and 42 = 63 ✓
✓
x = 4.
SMART APPROACH
विकल्प रखकर देखें: x = 4 पर 42 = 2 और 63 = 2 ✓। उत्तर 4।
Put the options: x = 4 gives 42 = 2 and 63 = 2 ✓. Answer 4.
Source: Selection Post Phase XIV (Graduate) · 19 Sep 2026 · Shift 1। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (Graduate) · 19 Sep 2026 · Shift 1. Solution by Prashant Sir, from Vijayastra.