*Sy g peduli kalau u gk bisa B.Ing, kalau g bisa, g usah jawab. Dan y, sy kls Biling, jd soal brbhsa Eng.
When the blue tiles add up to 10,000 tiles, there are 404 white tiles.
Problem
Mr. Yudi made several square-shaped pool designs. Each pool has a square-shaped water storage area which is tiled in blue. Around the pool, white tiles are installed. The following image shows the design of the three smallest pools.
(The mentioned image is on the question box.)
How many white tiles are there, when the blue tiles add up to 10,000 tiles?
Solution
Based on that image, we can get that the [tex]n[/tex]-th pool has:
- [tex]B_n=n^2[/tex] blue tiles, and
- [tex]T_n=(n+2)^2[/tex] tiles in total (blue and white).
Thus, the number of white tiles on the [tex]n[/tex]-th pool can be obtained by:
[tex]\large\text{$\begin{aligned}W_n&=T_n-B_n\\&=(n+2)^2-n^2\\&=n^2+4n+4-n^2\\&=4n+4\\W_n&=4(n+1)\end{aligned}$}[/tex]
When the blue tiles add up to 10,000 tiles, [tex]n =\sqrt{10,000}=100[/tex].
Hence,
[tex]\large\text{$\begin{aligned}W_{100}&=4(100+1)\\&=4\times 101\\&=\boxed{\bf\,404\,}\ \sf white\ tiles\end{aligned}$}[/tex]
[tex]\blacksquare[/tex]
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