A rectangular room is 3m longer than it is wide.
It costs 364 pounds to carpet the room. Carpet costs 16 pounds per square metre.
How wide is the room?
w(w+3)*16 = 364
now just solve for w.
Area = 364/16 = 22.75 m^2
Width = W meters.
Length = W+3 meters.
Area = (W+3) * W = 22.75
W^2 + 3W - 22.75 = 0
Use Quadratic Formula:
W = 3.5 meters = Width.
To find the width of the room, we can set up an equation based on the given information.
Let's say the width of the room is "x" meters.
According to the problem, the length of the room is 3 meters longer than the width. Therefore, the length would be "x + 3" meters.
The area of the rectangular room can be calculated by multiplying the width and length:
Area = width × length
So, the area of the room is:
Area = x × (x + 3)
The cost to carpet the room is given as 364 pounds, and the carpet costs 16 pounds per square meter. Therefore, we can set up another equation:
Cost = Area × Carpet Cost per square meter
Substituting the values we have, we get:
364 = x × (x + 3) × 16
Now, we can solve this quadratic equation to find the width of the room.
To solve the equation, we can simplify it further:
364 = 16x^2 + 48x
Rearranging the equation:
16x^2 + 48x - 364 = 0
Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Simplifying the equation further, we divide through by 4:
4x^2 + 12x - 91 = 0
Now, we can factor the equation:
(2x - 7)(2x + 13) = 0
Setting each factor equal to zero:
2x - 7 = 0 or 2x + 13 = 0
Solving for x, we get:
2x = 7 or 2x = -13
Dividing by 2:
x = 7/2 or x = -13/2
Since the width of a room cannot be negative, we discard the negative value.
Therefore, the width of the room is 7/2 = 3.5 meters.