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

Answer:

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

Step-by-step explanation:

Given portrait without frame has a height of $1.5\times w$

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 $1.5\times w$

Now, height of frame is

$1.5\times w+3+3\\\\=1.5\times w+6$

As the frame is in rectangular shape,  

Total area of frame would be

$2\times$Height of frame $\times$ width of frame $+$ $2\times$ Width of portrait $\times$ width of frame.

$(2\times(1.5\times w)+6)3+(2\times w\times3)\\\\=6((1.5\times w)+6)+(6\times w)\\\\=(9\times w)+36+(6\times w)\\\\=(15\times w)+36$

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