Answer:
w = 3/2
Step-by-step explanation:
Area of a Rectangle
The 5-inch by 7-inch picture has a frame of width w surrounding all four sides.
a)
The total length of the framed picture is 7 + 2w
The total width of the framed picture is 5 + 2w
b)
The total area of the framed picture is:
At = (7 + 2w)(5 + 2w)
c) We know the total area is 80 square inches, thus:
(7 + 2w)(5 + 2w) = 80
Operating:
[tex]35 + 14w + 10w + 4w^2=80[/tex]
Simplifying:
[tex]4w^2 + 24w -45 =0[/tex]
We now write:
[tex]4w^2 + 30w - 6w -45 =0[/tex]
Factor out 2w from the first two terms and -3 from the last two terms:
[tex]2w(2w + 15) - 3(2w + 15) =0[/tex]
Factor out 2w+15
(2w + 15)(2w - 3)=0
The solutions are:
w = -15/2
w = 3/2
The only feasible solution is the positive value, thus
w = 3/2