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Find the perimeter when 84 triangles are put together in the pattern shown below. Assume that all triangle sides are 1 cm long.

Find the perimeter when 84 triangles are put together in the pattern shown below. Assume that all triangle sides are 1 cm long. class=

Answer :

Answer:

86 cm.

Step-by-step explanation:

If we add  1 more triangle to one in the picture we that:

If we  place 6 triangles together  the perimeter will be  6 + 2 = 6

for 8 triangles the perimeter is 10 .

For 84 the perimeter will be 86 cm.

adioabiola

Here, we are required to determine the perimeter of 84 triangle arranged in the pattern as in the attached image.

  • The perimeter of 84 triangles put together in that pattern is 86cm

Since , the triangles are equilateral triangles as all sides are 1cm long.

By observation; The perimeter of one of the triangles is : 3 × 1cm = 3cm.

Upon addition of a second triangle; the perimeter becomes; 4 × 1cm = 4cm.

And when a 3rd triangle is added, the perimeter becomes; 5 × 1cm = 5cm.

Therefore, the perimeter of the consecutive number of triangles can be modelled into an arithmetic progression (a.p) with;

  • First term = a = 3cm
  • Common difference, d = 4 - 3 = 1cm

T(n) = a + (n - 1)d

As a result; the 84th term is given as;

T(84) = 3 + (84 - 1) × 1

T(84) = 86cm

Therefore, the perimeter of 84 triangles arranged in that pattern is 86cm.

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