Answer:
Area = [tex]1.5w^2+15w+36[/tex]
Step-by-step explanation:
Let the width of portrait be 'w'
Given:
Height of portrait without frame (h) = 1.5 times its width = [tex]1.5w[/tex]
Width of the frame is 3 inches on all sides.
Area of the framed portrait is the total area of the portrait plus the area of the frame.
The figure representing the above scenario is shown below.
From the figure, area of rectangle ABCD is the area of the framed portrait.
From the figure,
AB = [tex]3 + w + 3 = w + 6[/tex]
BC = [tex]3 + h + 3 = h + 6 = 1.5w + 6[/tex]
Now, area of the rectangle ABCD is given as the product of the length AB and width BC. Therefore,
[tex]Area=AB\times BC\\\\Area=(w+6)(1.5w+6)\\\\Area=(w\times 1.5w)+(w\times 6)+(6\times 1.5w)+(6\times 6)\\\\Area=1.5w^2+6w+9w+36\\\\Area=1.5w^2+15w+36[/tex]
Therefore, the expression for the area of the framed portrait in terms of the width 'w' is given as:
Area = [tex]1.5w^2+15w+36[/tex]
The area of the portrait without the frame will be [tex]A=13.5=1.5w^2[/tex].
Given information:
A portrait without its frame has a height 1.5 times its width w, in inches.
The width of the frame is 3 inches.
Length of the frame will be,
[tex]l=1.5w\\l=1.5\times 3\\l=4.5[/tex]
So, the area of portrait without frame will be,
[tex]A=l\times w\\A=1.5w\times w\\A=1.5w^2\\A=1.5\times 9=13.5=1.5w^2[/tex]
Therefore, the area of the portrait without the frame will be [tex]A=13.5=1.5w^2[/tex].
For more details, refer to the link:
https://brainly.com/question/15218510
