Question

A square floor has a side length of 7x5y6 units. A square tile has a side length of x2y units. How many tiles will it take to cover the floor? Express your answer in simplified form.

Answer 1

It will take $49x^{6}y^{10}$ tiles to cover the floor

Given the following:

side length of the square floor - $7x^5y^6$ units

side length of square tile - $x^2y$ units

First, find the area of the square floor and square tile:

Area of the square floor = area of a square = $s^2$

Where, $s = 7x^5y^6$

Plug in the value into the formula

Area of the square floor $= (7x^5y^6)^2$

$= 49x^{10}y^{12}$ sq units

Area of the square tile = area of a square = $s^2$

Where, $s = x^2y$

Plug in the value

Area of the square tile $= (x^2y)^2$

= $x^4y^2$ 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.

$= \frac{ 49x^{10}y^{12}}{x^4y^2}$

Simplify

$= 49x^{6}y^{10}$

The number of tiles to cover the floor would be expressed as $= 49x^{6}y^{10}$ tiles

Learn more about area of a square here:

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