Mathematics

In the given figure, $DE\parallel BC$. If $AD=xcm, DB=(x-2)cm, AE=(x+2)cm$ and $EC=(x-1)cm$, find the value of $x$.

$x=4$

SOLUTION
Given: AD = 3.6 cm, AB = 9 cm and AE = 2.4 cm $DE \parallel BC$
Since, $DE \parallel BC$, by Equal Intercept Theorem,
$\frac{AD}{BD} = \frac{AE}{EC}$
$\frac{x}{x - 2} = \frac{x + 2}{x - 1}$
$x (x - 1) = (x - 2) (x + 2)$
$x^2 - x=x^2 - 4$
$x=4$

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Single Correct Medium Published on 09th 09, 2020
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