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Chapter 12: Q. 61 (page 817)

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

Expert verified

Total number of beige tiles required = 210

Total number of blue tiles required = 190

Step by step solution

01

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 .

02

Step 2: 

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

So the sum is S20=1+2+3.......20

Now we use sum formula

role="math" localid="1646974408795" Sn=n2(2a+(n-1)d)a=1,commondifferenced=1n=20S20=202(2(1)+(20-1)1)S20=202(21)S20=210

Total number of beige tiles required = 210

03

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

Sn=n2(2a+(n-1)d)a=1,commondifferenced=1n=19S20=192(2(1)+(19-1)1)S20=192(20)S20=190

Total number of blue tiles required = 190

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