# 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?

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

#### Explanation:

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:

$A r e a = b a s e \times w i \mathrm{dt} h$

$A r e a = 11 \times 6 = 66$ 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:

$A r e a = \left(11 + 8\right) \times \left(6 + 8\right) = 19 \times 14 = 266$ square feet, an addition of 200 square feet.

Sep 7, 2016

$\left(1\right) : \text{The New Area="2(2x^2+49x+297)"sq.ft.}$

$\left(2\right) : \text{Addition in Area="2(2x^2+49x+264)"sq.ft.}$

#### Explanation:

The length of the living room is $11 '$

After extension of $\left(x + 8\right) '$ on each side,

the new length becomes $11 + \left(x + 8\right) + \left(x + 8\right) = \left(2 x + 27\right) '$

Similarly, the new width is $\left(2 x + 22\right) '$

Hence, $\text{The New Area=new length"xx"new width}$

$= \left(2 x + 27\right) \left(2 x + 22\right)$

$= {\left(2 x\right)}^{2} + \left(27 + 22\right) \left(2 x\right) + \left(27 \times 22\right)$

$= 4 {x}^{2} + 98 x + 594$

$= 2 \left(2 {x}^{2} + 49 x + 297\right) \text{sq.ft.}$

Prior to the Extension,

the Arrea of the Living Room$= 6 ' \times 11 ' = 66 \text{sq.ft}$

Hence, due to Extension,

$\text{Addition in Area= New Area - Old Area}$

$= \left(4 {x}^{2} + 98 x + 594\right) - \left(66\right)$

$= 4 {x}^{2} + 98 x + 528$

$= 2 \left(2 {x}^{2} + 49 x + 264\right) \text{sq.ft.}$