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 $$x$$.


ANSWER

$$x=4$$


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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