SOLUTION: The width of a room is 4m less than the length, if the area is 45sq meters, find the dimension of the room

Question 761135: The width of a room is 4m less than the length, if the area is 45sq meters, find the dimension of the room
Found 2 solutions by Stitch, Cromlix:
Answer by Stitch(470) (Show Source): You can put this solution on YOUR website!
The equation for the area of a rectangle is A = L x W
Equation 1:
Equation 2:
Plug (L-4) into equation 1 for W

Multiply the L through

Set the equation to zero by subtracting 45 from both sides

You can now factor the equation by hand or use the quadratic equation.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=196 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9, -5. Here's your graph:

The quadratic shows us that when L is equal to -5 and 9. Since we can not have a negative distance, 9 is th eonly answer that makes sense.
Now plug 9 into equation 2 for L
Equation 2:

----------------------------
L = 9m
W = 5m
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Length = x
Width = x - 4
Area = length * width
x(x - 4) = 45
x^2 - 4x = 45
x^2 - 4x - 45 = 0
(x - 9)(x + 5) = 0
x = -5 (no answer)
x = 9
Length = 9m
Width = 5m
Hope this helps.
:-)
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