Answer
$AC = 16$
$BD = 16$
Work Step by Step
According to Theorem 6-15, the diagonals of a rectangle are congruent. Therefore, we can set $AC$ and $BD$, the diagonals of $ABCD$, equal to one another to solve for $x$:
$AC = BD$
Substitute with the expressions given for each diagonal:
$2(x - 3) = x + 5$
$2x - 6 = x + 5$
Subtract $x$ from each side of the equation to move variables to the left side of the equation:
$x - 6 = 5$
Add $6$ to each side of the equation to solve for $x$:
$x = 11$
Now that we have the value of $x$, we can plug $11$ in for $x$. We do not need to evaluate both expressions because we know that the length of the two diagonals are equal to one another:
$BD = 11 + 5$
Add to solve:
$BD = 16$
