Question

An area is paved with square tiles $o$ as cetain size and the required is $600$. If the tiles had been $1cm$ smaller each way, $864$ tiles would have been needed to pave the same area. Find the size of the larger tiles.

Answer 1

Let we have square tiles of a certain length, which we will call ${}^{\prime }{x}^{\prime }cm.$

The area of each tile is $x^{2}c{m}^2$.

The total area paved would be $600x^2$ $c{m}^2$.

According to given question,

$600x^2=864{(x-1)}^2$

$\Rightarrow 600x^2=864x^2-1728x+864$

$\Rightarrow 264x^2-1728x+864=0$

$\Rightarrow 24(11x^2-72x+36)=0$

$\Rightarrow 11x^2-66x-6x+36=0$

$\Rightarrow 11x(x-6)-6(x-6)=0$

$\Rightarrow (x-6)(11x-6)=0$

$\Rightarrow x-6=0,11x-6=0$

$\Rightarrow x=6or\frac{6}{11}$

Hence, the length of tiles$=x=6cm.$

Hence, this is the answer.