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Anonymous asked in Science & MathematicsMathematics · 2 months ago

Math Quadratic Equations?

A family plans to have the hardwood floors in their square dining room re-finished, and new baseboards installed. The cost of re-finishing the hardwood floors is $5.75 per square foot and the cost of purchasing and installing the new baseboard is $14 per linear foot. If the family paid $1135, you have to find out dimensions of the room.

What is the length of the dinning room? 

I figured out that the width is 10 but I cannot figure out what equation to use to find the length. 

3 Answers

  • 2 months ago

    Given a Square Dining Room:

    let x --> be dimensions [ both length and width ]

    x^2 = Area

    2 *( x+ x) = Perimeter

    => 5.75x² = Flooring cost

         14*2*(x + x ) = cost of baseboard

    => 5.75x² + 14*4x= 1135

        5.75x² + 56x - 1135 = 0

    Using the quadratic equation:

    Floors are    x =   - b ±√(b² - 4ac)/2a

                        -56 ±√(56² - 4(5.75)(-1135))/2(5.75)

                      x = 10 or 19.73

                     x = 10 is the best size for your money

  • ?
    Lv 7
    2 months ago

    The room is square.

  • Bryce
    Lv 7
    2 months ago

    Let x= one side of the room.

    5.75x² + 14*4x= 1135

    5.75x² + 56x - 1135= 0

    x= 10 ft

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