Question

A line segment AB of length 2 metre is divided at a point C into two parts such that AC^2 =AC×CB. Find the length of BC

Answer 1

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Answer 2

Answer:

The length of BC is 1 meter.

Step-by-step explanation:

Given information: AB=2 meter, point C divides the line segment AB into two parts such that AC^2 =AC×CB.

$AC^2=AC\times CB$

$AC^2-AC\times CB=0$

$AC(AC-CB)=0$

Using zero product property, we get

$AC=0$

$AC-CB=0\Rightarrow AC=CB$

Since point C divides the line segment AB into two parts, so AC can not be 0. it means AC=CB or C is the midpoint of AB.

$AB=AC+BC$

$AB=BC+BC$                       (AC=BC)

$AB=2BC$

Substitute AB=2 in the above equation.

$2=2BC$

Divide both sides by 2.

$1=BC$

Therefore, the length of BC is 1 meter.