Question

a segment BC of length 4 m is divided by point D in two parts such that BD^2=DC × BC find the length of DC.

Answer 1

Answer:

Length of DC is $6-2\sqrt5\:m$

Step-by-step explanation:

Given:

BC = 4 m

Let BD = x

Then DC=4-x

$BD^2=DC*BC$

$\implies\:x^2=(4-x)*4$

$\implies\:x^2=16-4x$

$\implies\:x^2+4x-16=0$

To find x, we solve this equation

$\implies\:x^2+4x-16=0$

$x^2+4x=16$

$x^2+4x+4=16+4$

$(x+2)^2=20$

$x+2=$±$2\sqrt5$

$x=-2$±$2\sqrt5$

But x cannot be negative

$x=-2+2\sqrt5$

$x=2\sqrt5-2$

Now,

$DC=4-(2\sqrt5-2)$

$DC=4-2\sqrt5+2$

$DC=6-2\sqrt5\:m$