Question

John creates a painting on a rectangular canvas with a width that is two inches longer than the height, as shown in the diagram below.

(It is a rectangle with h+2 on the bottom and h on the side)

A. Write a polynomial expression, in simplified form, that represents the area of the canvas. (1 point)
B. John adds a 3-inch-wide frame around all sides of his canvas. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame. (1 point

Answer 1

Given:

h = height of the rectangular canvas
h + 2 = width of the rectangular canvas

The polynomial expression that represents the area of the canvas:

A = height x width
= h * (h+2)
A = h^2 + 2h

If John adds a 3-inch-wide frame around all sides of his canvas, the new height and width are:

h + (3*2) = h + 6 = height
h + 2 + 6 = h + 8 = width

Anew = (h +6) (h +8)
= h^2 +14h +48