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In ∆ABC, D and E are …

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In ∆ABC, D and E are poonts on sides AB and AC respectively such that DE || BC. If AD=x, DB=x-2, AE=x+2, EC=x-1, than find the value of 'x'.

Posted by Chanchal Dhiman 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given in triangle, {tex}{/tex}ABC DE {tex}\|{/tex} BC
{tex}\frac { \mathrm { AD } } { \mathrm { DB } } = \frac { \mathrm { AE } } { \mathrm { EC } }{/tex} (by BPT)

{tex}\Rightarrow \quad \frac { x } { x - 2 } = \frac { x + 2 } { x - 1 }{/tex}
{tex}\Rightarrow{/tex} x(x - 1) = (x + 2)(x - 2)
{tex}\Rightarrow{/tex} x² - x = x² - 2² {tex}\Rightarrow{/tex} x² - x = x² - 4
{tex}\Rightarrow{/tex} x = 4

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