Answer
$x=12$
Side lengths:
$2x-2=15$
$x-2=10$
Work Step by Step
The perimeter is the sum of the length of all sides. This rhombus has two sides with a length of $2x-9$ each and two sides with a length of $x-2$ each, therefore:
$Perimeter=50=2(2x-9)+2(x-2)$
Apply the distributive property:
$50=4x-18+2x-4$
Group the terms with x as a common factor:
$50=(4+2)x-18-4$
Do the additions:
$50=6x-22$
Add 22 to each side of the equation:
$72=6x$
Divide both sides by 6:
$x=12$
The side lengths are then:
$2x-2=2\cdot12-9=24-9=15$
$x-2=12-2=10$
