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Submitted by casy.k1 on Thu, 2013-05-02 20:02
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# The width of a rectangular painting is 3in. more than twice the height. A frame is 2.5 in. wide goes...

The width of a rectangular painting is 3in. more than twice the height. A frame is 2.5 in. wide goes around the painting. Write and expression for the area of the painting and frame?

Submitted by mathsexpert on Thu, 2013-05-02 23:58
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let height xx painting = x in.

xx  width  of xxxxxxxx x xxx + x ) xxx

xxxxxx xx painting = xxxxx . height

xx xx xx xx   xx xx   xx     xx   xx xx = xxx x 3) x x

xx   xx xx   xx xx xx     xx xx xx   xxx xx2 + 3x

xxxxxxxxxxxx xx painting xxxxxxxxx xxxxx x (x + 2 . xxxx xxxxx   , xxxx xxxxx of frame is on xxxx sides

xx     xx xx       xx   xx xx     xx     xx   xx xx xx     xx       xx xx xx = ( x + x ) in.

xx  width xxxx xxxxxxxxxxxxxxxxxxxxx xxxxx x xxx x 3 + 2 . xxxx  in xx xxx width of frame xx xx xxxx xxxxx

xx   xx   xx xx xx   xx xx xx     xx     xx xx   xx   xx   xx   xx       xx xx xx   xx (2x x 3 + 5 x xxx

xx       xx         xx xx         xx             xx xx xx xx   xx xx     xx   = x 2x + 8) xxx xx xxxx

area of xxxxxxxxxxxxxxxxxxxxx frame x xxxxx x xxxxxx

xx     xx xx xx xx     xx   xx   xx xx       xx           xx   xx xx   xx xx xxx xx + xx x xx + xx  in

xx     xx     xx     xx xx     xx     xx     xx xx xx   xx     = 2xx + 8x x 10x x xx

xx xx xx       xx xx   xx xx   xx xx     xx         xx   xx   xx       xx xx xx x  2xxxxx 18x x xx

xx   area xx frame = area of xxxxxxxx including xxxxx - xxxx of xxxxxxxx

xx xx   xx xx     xx xx xx   xx xx  = ( 2xxxxx 18x x xxx - ( xxx x 3x)

xx   xx   xx   xx       xx xx xx =   2xx + xxx + 40 - 2xxxxxxxxx

xx xx xx xx   xx xx   xx xx     xx   x xxxxxx + xxx xxxxxx