Question

in the figure below, points $a$, $d$, and $c$ are collinear.
find the value of $x$.
$ab = 3.82$in
$bc = x$
$ad = 2.1$in
$cd = 2.1$in

Explanation:

Step1: Identify triangle properties

Since \(AD = CD = 2.1\) in and \(BD\perp AC\) (right angle at \(D\)), \(BD\) is the perpendicular bisector of \(AC\). So, \(\triangle ABC\) is isosceles with \(AB = BC\).

Step2: Determine \(x\) value

Given \(AB = 3.82\) in and \(BC = x\), by the property of isosceles triangle (perpendicular bisector implies equal sides), \(x = AB\).
So, \(x = 3.82\) in.

Answer:

\(x = 3.82\) inches