Respuesta :

absor201

Answer:

The expression to represent the length

  • [tex]length=\frac{4\left(x-4\right)}{x}[/tex]                      

Step-by-step explanation:

Given

  • Area = x-16/x
  • Width = x/4+1
  • Length =?

We know that The formula for the area of the rectangle is:

  • Area =  Length x Width

Thus, the length of a rectangle

Length = Area ÷ Width

            [tex]=\frac{x-\frac{16}{x}}{\frac{x}{4}+1}[/tex]

            [tex]=\frac{x-\frac{16}{x}}{\frac{x+4}{4}}[/tex]

            [tex]=\frac{\frac{x^2-16}{x}}{\frac{x+4}{4}}[/tex]

[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]

             [tex]=\frac{\left(x^2-16\right)\cdot \:4}{x\left(x+4\right)}[/tex]

             [tex]=\frac{\left(x+4\right)\left(x-4\right)\cdot \:4}{x\left(x+4\right)}[/tex]

Cancel the common factor: (x+4)

            [tex]=\frac{4\left(x-4\right)}{x}[/tex]

Thus, the expression to represent the length

  • [tex]length=\frac{4\left(x-4\right)}{x}[/tex]                      

Otras preguntas