What is the perimeter of this rectangle?

As the shape is declared to be a rectangle, then ...

$$y=x-14$$

and

$$x=2y+2$$

Rearranging the second equation to the same structure as the first.

$$2y=x-2$$

Subtracting the first equation from the second

$$y=12$$

Substituting this into the first equation

$$12=x-14$$ $$x=26$$

The perimeter of a rectangle is given by

$$P=2(l+w)$$ $$P=2(x-14+x)$$ $$P=4x-28$$ $$P=76$$

-oOo-

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Further Reading:

Simultaneous Equations
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