Question

Creating a Mosaic A mosaic is designed in the shape of an equilateral triangle, 20 feet on each side. Each tile in the mosaic is in the shape of an equilateral triangle, 12 inches to a side. The tiles are to alternate in color as shown in the illustration. How many tiles of each color will be required?

Short answer

Total number of beige tiles required = 210

Total number of blue tiles required = 190

Step-by-step solution

Given information 

Equilateral triangle is 20 ft each on each side. Each tile in the mosaic is in the shape of an equilateral triangle, 12 inches to a side. Top row is 1 tile and bottom row has 20 tiles .

Step 2: 

From the given diagram , each row is increased by 1.

So the sum is $S_{20}=1+2+3.......20$

Now we use sum formula

role="math" localid="1646974408795" $$\begin{gathered} S_n=\frac{n}{2}(2a+(n-1\left)d\right) \\ a=1,commondifferenced=1 \\ n=20 \\ {S}_{20}=\frac{20}{2}\left(2\right(1)+(20-1\left)1\right) \\ {S}_{20}=\frac{20}{2}\left(21\right) \\ {S}_{20}=210 \end{gathered}$$

Total number of beige tiles required = 210

Blue tiles

First row has 1 blue tile . there are 19 rows of blue tiles. each row is increasing by 1

a=1, n=19 and d=1

$$\begin{gathered} S_n=\frac{n}{2}(2a+(n-1\left)d\right) \\ a=1,commondifferenced=1 \\ n=19 \\ {S}_{20}=\frac{19}{2}\left(2\right(1)+(19-1\left)1\right) \\ {S}_{20}=\frac{19}{2}\left(20\right) \\ {S}_{20}=190 \end{gathered}$$

Total number of blue tiles required = 190