The length of a rectangle is $3x+10$ feet and its width is $x+12$ feet.  If the perimeter of the rectangle is 76 feet, how many square feet are in the area of the rectangle?
The perimeter of a rectangle with dimensions $l$ and $w$ is $2(l+w)$.  Setting $2(3x+10+x+12)$ equal to 76, we find $4x+22=38$, which implies $x=4$ feet.  The area of the rectangle is $(3x+10)(x+12)=(3(4)+10)(4+12)=\boxed{352}$ square feet.