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)   (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 (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=360000 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.2, 6. Here's your graph:
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