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 $2.25 per square foot and the cost of purchasing and installing the new baseboards $14.5 per linear foot. If the family paid $1773, you have to find out dimensions of the room.

Dimension of room = 18 foot x 18 foot

Step-by-step explanation:

Let the square room is of side a foot,

The cost of re-finishing the hardwood floors is $2.25 per square foot and the cost of purchasing and installing the new baseboards $14.5 per linear foot

Total cost is $1773.

Cost for re-finishing the hardwood floors = Area x 2.25

Area = a²

Cost for re-finishing the hardwood floors = 2.25 a²

Cost of purchasing and installing the new baseboards = Perimeter x 14.5

Perimeter = 4a

Cost of purchasing and installing the new baseboards = 4a x 14.5 = 58 a

Total cost = Cost for re-finishing the hardwood floors + Cost of purchasing and installing the new baseboards

1773 = 2.25 a² + 58a

2.25 a² + 58a - 1773 = 0

a = 18 or a = - 43.77 (not possible)

Dimension of room = 18 foot x 18 foot