Question

A hall can be paved with $200$ square tiles of a certain size. If each tile were $5cm$ longer each way it would take $128$ tiles. Find the length of each tile.

Answer 1

let the area of hass is $A$

$A=200a^2$ where $a$ is side of one tile

Also

$A=128{(a+b)}^2$ where side is now $5cm$ length

$200a^2=128{(a+b)}^2$

$25a^2=16a^2+160a+400$

$9a^2-160a-400=0$

$9a(a-20)+20(a-20)=0$

$a$ can't be negative

$a-20=0$

$a=20cm$

Length of each tile $=20cm$