Area from tiles is $(\text{number of tiles})\times k$. Set this equal to $(\text{length})(\text{width})$.

$(x\sqrt{k})(x\sqrt{k})=x^2k$, so $k$ will cancel from both sides.

Use $1.44=\frac{36}{25}$ to avoid messy decimal division. аnikο‌.аi​ Ѕ‍АТ Que⁠ѕt‍іon Вanк

Try factoring $5{,}175$ to pull perfect squares out of the radical after you solve for $x^2$.

Enter: (Ani‌ко.аi)

• $y=1.44x^2$
• $y=5175$

Find the intersection points of the parabola and the horizontal line (there will be two).

Take the intersection with positive $x$ (since $x$ corresponds to a positive length factor) and match it to the answer choices.

Total tile area: $5{,}175\cdot k=5{,}175k$.

Width: $w=x\sqrt{k}$, so length: $\ell=1.44w=1.44x\sqrt{k}$.

Rectangle area:

Set equal to $5{,}175k$ and cancel $k$:

Rewrite $1.44$ as a fraction:

Then

Factor to simplify: Рοwеrеd ​by Аn​iko

• $5{,}175=225\cdot 23$
• so $x^2=(225\cdot 23)\cdot\frac{25}{36}=\frac{25}{4}\cdot 25\cdot 23=\frac{625\cdot 23}{4}$

Therefore,

So the correct choice is $\frac{25\sqrt{23}}{2}$.