Question

The width of a Rectangular painting is 3 inches more than twice the height. A frame that is 2.5 inches wide goes around the painting.
Write an expression in its simplest form for the area of the painting and the frame

Answer 1

Answer:

the answer is frame is= 6.2

Answer 2

The expression in its simplest form for the area of the painting and the frame is: $2h^2+18h+40$

Solution:

Let "h" be the height

Given that,

The width of a Rectangular painting is 3 inches more than twice the height

height = h

width = 3 + 2h

The frame is 2.5 inches all around, then adding 2.5 to each side, we have

height = h + 2.5 + 2.5 = h + 5

width = 3 + 2h + 2.5 + 2.5 = 8 + 2h

Now the area of the painting and the frame is given as:

$Combined\ area = (h+5) \times (8 + 2h)\\\\\Combined\ area = 8h + 2h^2 + 40 + 10h\\\\Combined\ area = 2h^2 + 18h + 40$

Thus the expression in its simplest form for the area of the painting and the frame is found

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