Question

In ABC, DE , find the value of x. IF AD=x DB=x+1 AE=3cm EC=5cm​

Answer 1

Given:

In Δ ABC, DE // BC, find the value of x. IF AD = x cm, DB = x + 1 cm, AE = 3 cm and EC = 5 cm.

To find:

The value of x

Solution:

We know that,

$\boxed{\bold{Thales\:Theorem\:/\:Basic \:Proportionality\:Theorem}}}:$  

If a line is drawn parallel to one of the sides of a triangle intersecting the other two sides at two distinct points, then the other two sides are divided in the same proportion.

Based on the Thales Theorem for Δ ABC since DE // BC, we get

$\frac{AD}{DB} = \frac{AE}{EC}$

on substituting AD = x, DB = x + 1, AE = 3 cm and EC = 5 cm, we get

$\implies \frac{x}{x + 1} = \frac{3}{5}$

$\implies 5x = 3(x + 1)$

$\implies 5x = 3x + 3$

$\implies 5x - 3x = 3$

$\implies 2x = 3$

$\implies \bold{x = 1.5\:cm}$

 

Thus, the value of x is → 1.5 cm.

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