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

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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) About Me  (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: 45+=+L%2AW
Equation 2: W+=+L+-+4
Plug (L-4) into equation 1 for W
45+=+L+%2A+%28L+-+4%29
Multiply the L through
45+=+L%5E2+-+4L
Set the equation to zero by subtracting 45 from both sides
0+=+L%5E2+-+4L+-+45
You can now factor the equation by hand or use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aL%5E2%2BbL%2Bc=0 (in our case 1L%5E2%2B-4L%2B-45+=+0) has the following solutons:

L%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A1%2A-45=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+196+%29%29%2F2%5Ca.

L%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+9
L%5B2%5D+=+%28-%28-4%29-sqrt%28+196+%29%29%2F2%5C1+=+-5

Quadratic expression 1L%5E2%2B-4L%2B-45 can be factored:
1L%5E2%2B-4L%2B-45+=+1%28L-9%29%2A%28L--5%29
Again, the answer is: 9, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-45+%29

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: W+=+L+-+4
W+=+%289%29+-+4
highlight%28W+=+5%29
----------------------------
L = 9m
W = 5m

Answer by Cromlix(4381) About Me  (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.
:-)