Question

A width of a rectangular painting is 3 in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting. Write an expression for the combined area of the painting and frame

Answer 1

The frame will go around all 4 sides of the painting.  That means that the length of each side of the painting will increase by 2.5 inches.  The height, h, will now be h + 5 (2.5  inches on the top and the bottom).  The width, 2h + 3, will now be 2h + 3 + 5 (again, 2.5 inches on the top and the bottom).  The area would be given by 
(h + 5)(2h + 3 + 5) = (h + 5)(2h + 8)
Multiplying this, we have:
h*2h + h*8 + 5*2h + 5*8 = 2h² + 8h + 10h + 40 = 2h² + 18h² + 40