Answer: [tex]\begin{gathered} 1e)\text{ }Area\text{ of the master bedroom = 18y}^2\text{ + 12y - 16} \\ 2e)\text{ }Perimeter\text{ of the master bedroom = 18y} \end{gathered}[/tex]
Explanation:
Given:
Master bedroom dimensions of 3y + 4 by 6y - 4
To find:
the perimeter and area of the master bedroom
The shape of the master bedroom is rectangular. To get the area of the bedroom, we will apply the area of a rectangle
[tex]Area\text{ of a rectangle = length }\times width[/tex][tex]\begin{gathered} let\text{ length = 6y - 4} \\ width\text{ = 3y + 4} \\ Area\text{ of the rectangle = \lparen6y - 4\rparen\lparen3y + 4\rparen} \\ \\ Expanding: \\ Area\text{ = }6y(3y\text{ + 4\rparen- 4\lparen3y + 4\rparen} \\ =\text{ }18y^2\text{ + 24y - 12y - 16} \\ collect\text{ like terms:} \\ =18y^2\text{ + 12y - 16} \\ \\ Area\text{ of the master bedroom = 18y}^2\text{ + 12y - 16} \end{gathered}[/tex]
To get the perimeter of the bedroom, we will apply the perimeter of a rectangle
[tex]Perimeter\text{ of a rectangle = 2\lparen length + width\rparen}[/tex][tex]\begin{gathered} let\text{ length = 6y - 4} \\ width\text{ = 3y + 4} \\ Perimeter\text{ of the rectangle = 2\lparen\lparen6y - 4\rparen + \lparen3y + 4\rparen\rparen} \\ =\text{ 2\lparen6y - 4 + 3y + 4\rparen} \\ =\text{ 2\lparen9y + 0\rparen} \\ =\text{ 2\lparen9y\rparen} \\ =\text{ 18y} \\ \\ Perimeter\text{ of the bedroom = 18y} \end{gathered}[/tex]
