38. A painting without its frame has
1 answer:
Answer:
1.5*w^2 + 15*w + 36
Step-by-step explanation:
We have to make the width of the portrait be 'w'
in addition to that the height of the frameless portrait (h) = 1.5 times its width, i.e. 1.5 * w
Frame width is 3 inches on all sides.
Therefore the 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.
I enclose a figure that allows us to see the problem better, the area of the rectangle ABCD is the area of the framed portrait.
From the figure, we have to:
AB = 3 + w + 3 = w + 6
BC = 3 + h + 3 = h + 6 = 1.5 * 2 +6
We know that the area of the rectangle ABCD is given as the product of the length AB and the width BC. Thus,
Area = (w + 6) * (1.5 * w + 6)
Area = 1.5 * w ^ 2 + 6 * w + 9 * w + 36
Area = 1.5*w^2 + 15*w + 36
That is, the expression for the framed portrait area in terms of the width 'w' is:
1.5*w^2 + 15*w + 36
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