Answer
$x = 4$
$MK = 4$
$JL = 4$
Work Step by Step
In the rectangle described, both $\overline{JL}$ and $\overline{MK}$ are diagonals of the rectangle. According to Theorem 6-15, diagonals of a rectangle are congruent to one another. Therefore, we can set the two expressions that are given for the two diagonals equal to one another:
$JL = MK$
Let's plug in our expressions for each diagonal:
$4x - 12 = x$
Add $12$ to each side of the equation to move constants to the right of the equation:
$4x = x + 12$
Subtract $x$ from each side to move variables to the left side of the equation:
$3x = 12$
Divide each side by $3$ to solve for $x$:
$x = 4$
Therefore, $MK = 4$.
Let's plug in $4$ for $x$ into the expression for $JL$:
$JL = 4(4) - 12$
Multiply first, according to order of operations:
$JL = 16 - 12$
Subtract to solve:
$JL = 4$
