Question 862546: 192 square tiles are needed to tile a kitchen wall. if the tiles had measured 2cm less each way, 300 tiles would have been needed. find the size of the larger tiles.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 192 square tiles are needed to tile a kitchen wall.
if the tiles had measured 2cm less each way, 300 tiles would have been needed.
find the size of the larger tiles.
:\
Let x = the side of the larger tile
then
192x^2 = the area of the wall
:
300(x-2)^2 = 192x^2
300(x^2 - 4x + 4) = 192x^2
300x^2 - 1200x + 1200 = 192x^2
300x^2 - 192x^2 - 1200x + 1200 = 0
A quadratic equation
108x^2 - 1200x + 1200 = 0
simplify, divide by 12
9x^2 - 100x + 100 = 0
Factors to
(9x - 10)(x - 10) = 0
the reasonable solution
x = 10 cm is the original size of the tiles
:
:
Check this, find the actual areas
192(10^2) = 19200 sq cm
300(8^2) = 19200
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