Answer:
[tex]A=3w^2+13w+100[/tex] [tex][in^2][/tex]
Step-by-step explanation:
To solve this problem, we call:
L = length of the picture
w = width of the picture
We know that the picture is 3 times longer than its width, so
L = 3w (1)
Also, we know that the frame around the picture is 5 inches wide. This means that the length of the picture + frame is
L' = L + 5 + 5 (because there are 5 inches on one side and 5 inches on the other side of the picture), so
L' = L + 10
And similarly, the total width is
w' = w + 10
Therefore, the total area will be:
[tex]A=L'\cdot w' = (L+10)(w+10)[/tex]
And using (1) we can rewrite it as
[tex]A=(3w+10)(w+10)[/tex]
Solving explicitely,
[tex]A=3w^2+13w+100[/tex] [tex][in^2][/tex]
