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John made a rectangle pen for his dog using 28 feet of fencing. If the width of the two more than one-half the length what is the length and width of The pen the length I’ve pen is

Respuesta :

calculista

Answer:

The length of the pen is [tex]8\ ft[/tex]

The width of the pen is [tex]6\ ft[/tex]

Step-by-step explanation:

Let

x-----> the length of the pen

y----> the width of the pen

we know that

The perimeter of the pen is

[tex]P=2(x+y)[/tex]

[tex]P=28\ ft[/tex]

so

[tex]28=2(x+y)[/tex]

[tex]14=(x+y)[/tex] ------> equation A

[tex]y=2+\frac{1}{2}x[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]14=x+(2+\frac{1}{2}x)[/tex]

[tex]14-2=\frac{3}{2}x)[/tex]

[tex]12=\frac{3}{2}x)[/tex]

[tex]x=12*2/3=8\ ft[/tex]

Find the value of y

[tex]y=2+\frac{1}{2}(8)=6\ ft[/tex]

therefore

The length of the pen is [tex]8\ ft[/tex]

The width of the pen is [tex]6\ ft[/tex]

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