A rectangular plot measuring $30$ m $\times$ $40$ m has a $2$ m wide pathway in the middle crosswise. Tiles of dimensions $30$ cm $\times$ $50$ cm are laid on the pathway in such a way so that no portion of these tiles cross the boundary of the pathway. How much area will still remain exposed after the maximum possible numbers of tiles are laid on the pathway without breaking any tiles?
This document shows answer as $1000$. However I am getting it as $4000$. Help!!!
On
Your answer 4,000Sq Cm is correct.
The pathway along 30M can be completely covered with 100 rows of 4 tiles each. The pathway along 40M is now divided into two areas of 2M by 19M each, that is, 200Cm by 1,900Cm each.Each of these sub-pathways can be covered by 63 rows of 4 tiles, covering 200Cm by 1,890Cm. That leaves each sub-pathway with 200Cm by 10Cm of uncovered area, which is 2,000Sq Cm. Total uncovered area is 4,000Sq Cm.
Okay, let's see. First things first, let's put in tiles so that we fill in, as much as possible, the straight portions of the pathway. We can take four tiles the long way and they'll fill up the path width. Then we get 18.9m along the longer straight path (which is 19m long), and 13.8m along the shorter straight path (which is 14 m long). Then we have a much smaller cross: a 2m square, with 10cm extra space in each direction one way, and 20cm extra space in each direction the other way.
This thing has an area of 5.2m^2; each block has an area of 0.15m^2, which add up (if you can fit 34 in this space) to 5.1m^2. So the question is this: Can we, in fact, fit 34 pieces in here?
The answer is yes.
This fits nicely into the space available, leaving only $10$ $100\text{ cm}^2$ areas uncovered, for a total of $1000\text{ cm}^2$ .