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You are building a dining room table for family dinners. The table has a length of 3x + 1 feet and a width of 3x - 1 feet. If the table has an area of 35 square feet, find the actual length and width.

Answer :

calculista

Answer:

Length 7 feet and Width 5 feet

Step-by-step explanation:

we know that

The area of the rectangle ( a dining room table) is equal to

[tex]A=LW[/tex]

where

[tex]L=(3x+1)\ ft[/tex]

[tex]W=(3x-1)\ ft[/tex]

[tex]A=35\ ft^2[/tex]

substitute

[tex]35=(3x+1)(3x-1)[/tex]

Apply difference of squares right side

[tex]35=9x^2-1[/tex]

[tex]9x^2=36\\x^2=4\\x=\pm2[/tex]

Remember that the length cannot be a negative number

so

x=2

Find the length

[tex]L=(3(2)+1)=7\ ft[/tex]

Find the width

[tex]W=(3(2)-1)=5\ ft[/tex]

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