Question

A square pool has a side length of s feet. How many 2-foot square tiles does it take to tile the border of the pool?

Answer 1

Given:

The length of the square pool is $s$ feet.

To find:

We need to find how many 2 foot square tiles required to tile the border of the pool.

Solution:

Before solving the question, first we should find the perimeter of the square pool.

We know that, perimeter of a square of length $x$ is $4x$.

So, the perimeter of the pool is $= 4 \times s = 4s$ foot.

Now, we will calculate the length of a 2 foot square tile.

Let $l$ be the length of 2 foot square tile.

The area of 2 foot square square tile is 2.

We know that, area of a square of length $x$ is $x^2$.

So, length of 2 foot square tile is

$\Rightarrow 2 = l^2$

$\Rightarrow l^2=2$

Applying square root on both sides,

$\Rightarrow \sqrt{l^2} =\sqrt{2}$

$\Rightarrow l =\sqrt{2}$ foot

So, the number of square tiles required to tile the border of the pool is

$\Rightarrow \frac{4s}{\sqrt{2}}$

$\Rightarrow \frac{2\times 2 \times s}{\sqrt{2}}$

$\Rightarrow \frac{\sqrt{2} \times \sqrt{2}\times 2 \times s}{\sqrt{2}}$

$\Rightarrow \sqrt{2}\times 2 \times s$

$\Rightarrow 2\sqrt{2} s$

Therefore, we need $2\sqrt{2} s$ tiles to tile the border of the pool.