Question

A portrait without its frame has a height 1.5 times its width w, in inches. The width of the frame is 3 inches on all sides. What is the area of the frame

Answer 1

The area of the frame is
`((15* w)+36)\ inch^2`

Explanation:

Given portrait without frame has a height of
`1.5* w`

Where
`w` is width of portrait.

Also, width of frame is
`3\ inches\ (Given)`

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
`3\ inches` two times into the height of the portrait.

So, initially height of portrait was
`1.5* w`

Now, height of frame is

`1.5* w+3+3\\\\=1.5* w+6`

As the frame is in rectangular shape,

Total area of frame would be

`2*`Height of frame
`*` width of frame
`+`
`2*` Width of portrait
`*` width of frame.

`(2*(1.5* w)+6)3+(2* w*3)\\\\=6((1.5* w)+6)+(6* w)\\\\=(9* w)+36+(6* w)\\\\=(15* w)+36`

The total area of the frame is
`((15* w)+36)\ inch^2`