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Farmer fernanda wants to put a fence around her rectangle field . The length of the field is 40 feet less than 3 times the width. If she has 320 feet of fencing, what are the dimensions of the field?

Respuesta :

calculista

Answer:

Length: 110 feet

Width: 50 feet

Step-by-step explanation:

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

where

L is the length of rectangle

W is the width of rectangle

we have

[tex]P=320\ ft[/tex]

so

[tex]320=2(L+W)[/tex] ----> equation A

[tex]L=3W-40[/tex] ----> equation B

Solve the system by substitution

substitute equation B in equation A

[tex]320=2(3W-40+W)[/tex]

solve for W

[tex]320=2(4W-40)[/tex]

[tex]320=8W-80[/tex]

[tex]8W=320+80[/tex]

[tex]8W=400[/tex]

[tex]W=50\ ft[/tex]

Find the value of L

[tex]L=3(50)-40=110\ ft[/tex]

therefore

The dimensions of the field are

Length: 110 feet

Width: 50 feet

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