Question

if $overline{cd}congoverline{de}$, $bc = 4u$, and $be = u + 66$, what is the value of $u$?

Explanation:

Step1: Use property of congruent segments

Since $\overline{CD}\cong\overline{DE}$ and the line perpendicular to $\overline{CE}$ at the mid - point (by the given congruence and right - angle) implies $BC = BE$ (by the property of perpendicular bisector of a line segment).
$4u=u + 66$

Step2: Solve the equation for $u$

Subtract $u$ from both sides of the equation.
$4u−u=u + 66−u$
$3u=66$
Then divide both sides by 3.
$u=\frac{66}{3}$

Answer:

$22$