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त्रिभुज

Question
CBSEHHIMAH10010128
Wired Faculty App

किसी समबाहु त्रिभुज में, सिद्ध कीजिए कि उसकी एक भुजा के वर्ग का तिगुना उसके एक शीर्षलंब के वर्ग के चार गुने के बराबर होता है।

Solution

           AB = AC [समबाहु ∆ है]
           angle straight B space equals space angle straight C space equals space 60 degree     [उभयनिष्ट]
और       angle ADB space equals space angle ADC space equals space 90 degree
           increment ABD space approximately equal to space increment ACD
rightwards double arrow            BD = DC
rightwards double arrow            BD space equals space DC space equals space 1 half BC
समकोण ∆ABD में,
             AB squared space equals space AD squared plus BD squared
rightwards double arrow          AB squared space equals space AD squared space plus space open parentheses 1 half BC close parentheses squared
rightwards double arrow          AB squared space equals space AD squared space plus space 1 fourth BC squared
rightwards double arrow          AB squared space equals space fraction numerator 4 AD squared plus BC squared over denominator 4 end fraction
rightwards double arrow         4 AB squared space equals space 4 AD squared plus BC squared
rightwards double arrow         4 AB squared space minus space BC squared space equals space 4 AD squared
rightwards double arrow         4 AB squared space minus space AB squared space equals space 4 AD squared space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket because AB space equals space BC space equals space AC right square bracket
rightwards double arrow          3 AB squared space equals space 4 AD squared

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