Question

You have been requested to display your family portrait in the lobby of the new Hampton inn in west Jordan it portrait measures x inches one side. and the other side is 2" longer than the other. the frame that surrounds the portraits is 2 inches wide.

You are planning on covering the frame with gold leaf to make it much brighter and so it can look better when it is displayed.

First: write the algebraic equation that will describe the area of the frame that needs to be covered.

Second: calculate how much gold leaf will you need if the shortest side of the portrait is 8 inches.

Answer 1

Start with this
portrait side 1=x
portrait side 2=x+2
frame=2 in

Answer 2

width of portrait --- x
length of portrait -- x+2

width of whole thing --- x+4
length of whole thing --- x+2 + 4 = x+6

area of portrait = x(x+2)
area of whole thing = (x+4)(x+6)

area of frame = (x+4)(x+6) - x(x+2)
= x^2 + 10x + 36 - x^2 - 2x
= 8x + 36

so when x=8 .........