What is the width and the length?

Question

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 $4.50 per square foot and the cost of purchasing and installing the new baseboard is $12 per linear foot. If the family paid $1224, you have to find out dimensions of the room. 

Answer 1

x represents the length of the room

y represents the width of the room

 

xy represents the area of the room

$4.50xy represents the cost of the flooring

 

2(x + y) represents the perimeter of the room

$12(2)(x + y) represents the cost of the baseboards

 

4.50xy + 24x + 24y = 1224

 

Two equations are needed to solve a system of two variables.

Is some relationship between the length and width of the room provided?