Perimeter is 2(a+b) where a and b are the lengths of the sides of the rectangle. We are told a=3b+2, so:
2(3b+2+b)=76; 2(4b+2)=76; 2b+1=76/4=19.
So 2b=18 and b=9, therefore a=3*9+2=29.
The length and width are therefore 9 and 29 inches.
The area is 9*29=261 sq in.