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the length of a rectangle is 4 units shorter than on-fourth of the width, x. Write an expression that represents the perimeter of the rectangle (Use one variable and a fraction) (MUST SHOW WORK PLEASE)

Respuesta :

kudzordzifrancis

ASNSWER


[tex]Perimeter=\frac{5x-16}{2}[/tex]

EXPLANATION

Let [tex]w=x[/tex] represent the width of the rectangle.


One-fourth of the width will be,

[tex]\frac{1}{4}x[/tex]


Let [tex]l[/tex] represent the length of the rectangle.

Then, subtracting 4 units from one-fourth the width gives us the length

[tex]\Rightarrow l=\frac{1}{4}x-4[/tex]


Perimeter[tex]=2x+2l[/tex]


[tex]\Rightarrow Perimeter=2x+2(\frac{1}{4}x-4)[/tex]



We expand to obtain;


[tex]Perimeter=2x+\frac{x}{2}-8[/tex]


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


[tex]Perimeter=\frac{5x-16}{2}[/tex]