Bradley is extending his rectangular living room. The original dimensions are 6 feet by 11 feet. If he extended his room by #x+8# feet, what is the new area? How many square feet of area did he add?

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Answer 1 · 2016-09-07T14:53:27

New room is 266 sq. ft for an addition of 200 sq. ft.

We've got a room that is being extended. The old room is 6 feet by 11 feet, which means that the area of the living room was:

#Area=base xx width#

#Area = 11 xx 6=66# square feet

We're extending the room by a factor of #x+8#, which means for each side, we're adding 8 feet. That looks like:

#Area=(11+8)xx(6+8)=19xx14=266# square feet, an addition of 200 square feet.

Answer 2 · 2016-09-07T15:02:51

#(1):"The New Area="2(2x^2+49x+297)"sq.ft."#

#(2):"Addition in Area="2(2x^2+49x+264)"sq.ft."#

The length of the living room is #11'#

After extension of #(x+8)'# on each side,

the new length becomes #11+(x+8)+(x+8)=(2x+27)'#

Similarly, the new width is #(2x+22)'#

Hence, #"The New Area=new length"xx"new width"#

#=(2x+27)(2x+22)#

#=(2x)^2+(27+22)(2x)+(27xx22)#

#=4x^2+98x+594#

#=2(2x^2+49x+297)"sq.ft."#

Prior to the Extension,

the Arrea of the Living Room#=6'xx11'=66"sq.ft"#

Hence, due to Extension,

#"Addition in Area= New Area - Old Area"#

#= (4x^2+98x+594)-(66)#

#=4x^2+98x+528#

#=2(2x^2+49x+264)"sq.ft."#