Question

एक समबाहु त्रिभुज ABC की भुजा 2a है। उसके प्रत्येक शीर्षलंब की लंबाई ज्ञात कीजिए।

Solution

समकोण ΔADB और ΔADC में,
विकर्ण AB = विकर्ण AC [दिया है]
AD = AD [उभयनिष्ट भुजा]

therefore space space space space space space space space increment ADB approximately equal to increment ADC

∴ BD = CD
=

space 1 half BC

[∵ जहाँ BC का मध्य बिंदु D है]

equals 1 half left parenthesis 2 straight a right parenthesis space equals space straight a

समकोण ΔADB में,

AD squared plus BD squared space equals AB squared

rightwards double arrow space space space space space space space space space AD squared space equals space AB squared minus BD squared space space space space space space space space space space space space space space space space space space space equals left parenthesis 2 straight a right parenthesis squared minus left parenthesis straight a right parenthesis squared space space space space space space space space space space space space space space space space space space space equals 4 straight a squared minus straight a squared space equals space 3 straight a squared rightwards double arrow space space space space space space space space space space AD space equals space square root of 3 straight a

इस प्रकार,

BE space equals space square root of 3 straight a

और

CF space equals space square root of 3 straight a

For Daily Free Study Material Join wiredfaculty