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Answer:
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Step-by-step explanation:
a) (h + 5)(2h + 8) is the expression for the combined area of the painting and frame
b) The combined area when h = 12 is 544 square inches
c) The combined area when h = 15 is 760 square inches
Solution:
Given that,
A frame that is 2.5 inches wide goes around the painting
The frame will go around all 4 sides of the painting.
That means that the length of each side of the painting will increase by 2.5 inches
Therefore,
The height of painting and frame is:
h = h + 2.5 + 2.5
h = h + 5
(2.5 inches on the top and the bottom)
Also given that,
Width of a rectangular painting is 3 inches more than twice the height
w = 3 + 2h
Now the width of painting and frame is:
w = 3 + 2h + 2.5 + 2.5
(Again, 2.5 inches on the top and the bottom)
w = 2h + 8
Thus the combined area of the painting and frame is:
B) Substitute h = 12 inches
Thus the combined area when h = 12 is 544 square inches
C) Substitute h = 15 inches
Thus combined area when h = 15 is 760 square inches