Question

The quadrilateral shown is a rectangle. What is the measure of CE?

Answer 1

Answer:

|CE|=2

Step-by-step explanation:

The quadrilateral is shown in the attachment

Recall that the diagonals of a rectangle are congruent.

This implies that:

|AC|=|BD|

We substitute the expressions to get:

$2x-6=5x-21$

This is now a linear equation in one variable.

Group similar terms to get:

$-6+21=5x-2x$

Simplify to get:

15=3x

Divide both sides by 3 to get:

$5=x$

Recall again that the diagonals of a quadrilateral bisect each other.

$|CE|=\frac{1}{2}|AC|$

$|CE|=\frac{1}{2}|2x-6|$

Plug x=5

$|CE|=\frac{1}{2}|2*5-6| =10-6=\frac{1}{2}*4=2$