Question

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 1

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

$A=LW$

where

$L=(3x+1)\ ft$

$W=(3x-1)\ ft$

$A=35\ ft^2$

substitute

$35=(3x+1)(3x-1)$

Apply difference of squares right side

$35=9x^2-1$

$9x^2=36\\x^2=4\\x=\pm2$

Remember that the length cannot be a negative number

so

x=2

Find the length

$L=(3(2)+1)=7\ ft$

Find the width

$W=(3(2)-1)=5\ ft$