Question 788273: one hundred tiles on certain size were used to pave a floor, if a tile which measures 4cm less on each side will be used, 225 tiles will be needed, find the size of the larger tile.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! one hundred tiles on certain size were used to pave a floor, if a tile which measures 4cm less on each side will be used, 225 tiles will be needed, find the size of the larger tile.
;
Let x = side of the larger tile
then
x^2 = area of the larger tile
and
(x-4)^2 = area of the smaller tile
:
225(x-4)^2 = 100x^2
:
225(x^2-8x+16) = 100x^2
:
225x^2 - 1800x + 3600 = 100x^2
:
225x^2 - 100x^2 - 1800x + 3600 = 0
:
125x^2 - 1800x + 3600 = 0
Simplify, divide by 25
5x^2 - 72x + 144 = 0
Factors to
(5x-12)(x-12)
Reasonable solution
x = 12 cm is the side of the larger tile
:
:
Check this by finding the area by each, should be the same
100*12^2 = 14400 sq/cm
225*8^2 = 14400 sq/cm
|
|
|
