SOLUTION: A square room and a hallway are to have carpet laid on the floor. 123 m^2 of carpet is required to cover both the hallway and the room. The width of the hallway is 6 m less than

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A square room and a hallway are to have carpet laid on the floor. 123 m^2 of carpet is required to cover both the hallway and the room. The width of the hallway is 6 m less than       Log On


   

Question 702684: A square room and a hallway are to have carpet laid on the floor.
123 m^2 of carpet is required to cover both the hallway and the room.
The width of the hallway is 6 m less than the length of the room.
The hallway is 5 m longer than the length of the room.
Write an equation showing this relationship and solve this equation to find the length of the room.
Can someone please answer this?
thanx
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Most of the solution process is drawing the picture and forming the equation.
Draw the area picture,
Scroll to see:


Total carpeting area for the floor is 123=X%5E2%2B%28X%2B5%29%2A%28X-6%29
and working from that,...find that....2X%5E2-X-153=0

Solution to quadratic formula: X=%281%2B-+sqrt%281-4%2A2%2A%28-153%29%29%29%2F%282%2A2%29
(Fill in the steps to compute the arithmetic)...
X=9, the length of the room.