SOLUTION: one hundred tiles of a certain size are needed to pave a floor. if a tile, which measures 4cm less on each side, will be used, 225 tiles will be needed. find the sizr of the larger

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Question 628503: one hundred tiles of a certain size are needed to pave a floor. if a tile, which measures 4cm less on each side, will be used, 225 tiles will be needed. find the sizr of the larger tile.
Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
We assume the tiles are square. Then 100*x*x is the area of the floor and. 100*x*x=225*(x-2)*(x-2). 100*x*x=225*(x*x-4*x+4). -125*x*x+900*x-900=0. If we solve this as shown below we get possible solutions of 1.2 and 6. Because we must be able to subtract 2 from x, 6 is the correct solution.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -125x%5E2%2B900x%2B-900+=+0) has the following solutons:

x%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=%28900%29%5E2-4%2A-125%2A-900=360000.

Discriminant d=360000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-900%2B-sqrt%28+360000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28900%29%2Bsqrt%28+360000+%29%29%2F2%5C-125+=+1.2
x%5B2%5D+=+%28-%28900%29-sqrt%28+360000+%29%29%2F2%5C-125+=+6

Quadratic expression -125x%5E2%2B900x%2B-900 can be factored:
-125x%5E2%2B900x%2B-900+=+-125%28x-1.2%29%2A%28x-6%29
Again, the answer is: 1.2, 6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-125%2Ax%5E2%2B900%2Ax%2B-900+%29