Question

Avi uses 11 toothpicks to form a row of 5 attached triangles, as shown. Suppose he continues this pattern, using 89 toothpicks in all. What is the total number of triangles formed? (sorry the picture wasn't uplodaing)

Answer 1

44

Explanation:

Given that Avi used 11 toothpicks to form a row of 5 attached triangles.

Total number of toothpicks used = 89

Let the total number of triangles formed be represented by x, so that:

11 toothpicks = 5 triangles

It would be observed that only the first triangle starting the pattern has 3 toothpicks. So that;

the average number of toothpicks for 1 triangle =
`(11)/(5)`

= 2.2

The number of toothpicks per triangle = 2.0

Thus,

x =
`(89)/(2.0)`

= 44.5

x = 44

The total number of triangles formed is 44.