Answer:
The area of the frame is [tex]((15\times w)+36)\ inch^2[/tex]
Step-by-step explanation:
Given portrait without frame has a height of [tex]1.5\times w[/tex]
Where [tex]w[/tex] is width of portrait.
Also, width of frame is [tex]3\ inches\ (Given)[/tex]
Now, we will compute the height of the frame
In order to find the total height of frame we need to add the width of frame [tex]3\ inches[/tex] two times into the height of the portrait.
So, initially height of portrait was [tex]1.5\times w[/tex]
Now, height of frame is
[tex]1.5\times w+3+3\\\\=1.5\times w+6[/tex]
As the frame is in rectangular shape,
Total area of frame would be
[tex]2\times[/tex]Height of frame [tex]\times[/tex] width of frame [tex]+[/tex] [tex]2\times[/tex] Width of portrait [tex]\times[/tex] width of frame.
[tex](2\times(1.5\times w)+6)3+(2\times w\times3)\\\\=6((1.5\times w)+6)+(6\times w)\\\\=(9\times w)+36+(6\times w)\\\\=(15\times w)+36[/tex]
The total area of the frame is [tex]((15\times w)+36)\ inch^2[/tex]
