A rectangular counter is covered with 600 square tiles. The counter could have been covered with 400 tiles 1 cm longer on a side. How do you find the length of a side of the smaller tile?

Mar 30, 2016

Answer:

The side length of the smaller tile is 2 cm

Explanation:

Let the length of 1 of the 600 tiles be ${L}_{t}$

Then Length of counter be ${L}_{c}$

S0$\text{ } {L}_{c} = 600 {L}_{t}$

But we are told the length of 1 of the 400 tiles is ${L}_{t} + 1 c m$

So we have:

$400 \left({L}_{t} + 1\right) = {L}_{c} = 600 {L}_{t}$

$400 {L}_{t} + 400 = 600 {L}_{t}$

$\implies {L}_{t} \left(600 - 400\right) = 400$

$\implies {L}_{t} = \frac{400}{200} = 2 c m$