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# 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

- jacob sLv 72 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