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Answered

A rectangular garden lot has an area of 2x + 11x + 12
If the width is x + 4 what is its length?​

Sagot :

LEVITHEMATHMAJORIN

Answer:

2x + 3

Step-by-step explanation:

  • Formula Needed:

A = lw

  • Where:

A is the Area of the Rectangle

l is the Length

w is the Width

  • Given:

A = 2x² + 11x + 12

w = x + 4

l = ?

  • Solution:

A = lw

(2x² + 11x + 12) = l(x + 4)

(2x² + 11x + 12)/(x + 4) = l(x + 4)/(x + 4)

l = (2x² + 11x + 12)/(x + 4)

[Solution of division in Picture]

l = 2x + 3

Therefore, the length is 2x + 3

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MYSTIFIEDBOYIN

[tex]\dag\:\underline{\sf AnsWer :}[/tex]

[tex]:\implies\sf Area \: of \: Rectangle = Length \times Breadth \\ \\ [/tex]

  • Area of rectangle = 2x² + 11x + 12
  • Width (Breadth) of rectangle = x + 4

[tex]\\\\:\implies\sf {2x}^{2} + 11x + 12 = Length \times x + 4 \\ \\ :\implies\sf Length = \dfrac{{2x}^{2} + 11x + 12 }{x + 4} \\ \\ :\implies\sf Length = \dfrac{{2x}^{2} + 8x + 3x + 12}{x + 4} \\ \\ :\implies\sf Length = \dfrac{2x(x + 4)+ 3(x + 4)}{x + 4} \\ \\ :\implies\sf Length = \dfrac{(2x + 3)( \cancel{x + 4})}{ \cancel{x + 4}} \\ \\ :\implies\gray{ \underline{ \boxed{\pink{\sf Length = 2x + 3 \: units}}}}\:\:\dag[/tex]

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