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?

Question

Maverick Smith · Accepted Answer

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.

Noah Atkinson · Answer

#(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."#

Aaliyah Anderson · Answer

undefined The new dimensions of Bradley's living room after extending it are $6 + (x + 8)$ feet by $11 + (x + 8)$ feet.

The new area of the living room is obtained by multiplying the new length by the new width, which gives:

$(6 + (x + 8)) \times (11 + (x + 8))$ square feet.

To find out how many square feet of area Bradley added, subtract the original area from the new area:

New area - Original area = $(6 + (x + 8)) \times (11 + (x + 8))$ - $6 \times 11$ square feet.

Simplify the expression to find the added area.