It will take [tex]49x^{6}y^{10}[/tex] tiles to cover the floor
Given the following:
side length of the square floor - [tex]7x^5y^6[/tex] units
side length of square tile - [tex]x^2y[/tex] units
First, find the area of the square floor and square tile:
Area of the square floor = area of a square = [tex]s^2[/tex]
Where, [tex]s = 7x^5y^6[/tex]
Plug in the value into the formula
Area of the square floor [tex]= (7x^5y^6)^2[/tex]
[tex]= 49x^{10}y^{12}[/tex] sq units
Area of the square tile = area of a square = [tex]s^2[/tex]
Where, [tex]s = x^2y[/tex]
Plug in the value
Area of the square tile [tex]= (x^2y)^2[/tex]
= [tex]x^4y^2[/tex] sq units
Next, find the number of tiles it will take to cover the floor by dividing the area of the square floor by the area of the square tile.
[tex]= \frac{ 49x^{10}y^{12}}{x^4y^2}[/tex]
Simplify
[tex]= 49x^{6}y^{10}[/tex]
The number of tiles to cover the floor would be expressed as [tex]= 49x^{6}y^{10}[/tex] tiles
Learn more about area of a square here:
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