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At Willow Creek Farms, Chrissy likes to stack the mandarins in triangular
pyramids. Each layer of mandarins is in the shape of an equilateral
triangle, and the top layer is a single mandarin.

Sagot :

michell96

In a pyramid eight layers high there are 120 tangerines stacked.

What is an equilateral triangle?

An equilateral triangle is a geometric figure that has three equal sides and all three internal angles are equal. According to this, the mandarin pyramid must have the same distance on all its sides.

So, in an 8-layer pyramid we can infer that layer 1 has 1 tangerine and it increases by 1 tangerine for each level, so in layer 8 they would have 8 tangerines.

On the other hand, if one of the sides of the triangle has a number of tangerines, it is possible to infer that the other sides will have the same number of tangerines since it is an equilateral triangle.

According to the above, it can be established that each layer of the pyramid is composed of the following number of tangerines:

  • Layer 1 - 1 tangerine
  • Layer 2 - 3 tangerines
  • Layer 3 - 6 tangerines
  • Layer 4 - 10 tangerines
  • Layer 5 - 15 tangerines
  • Layer 6 - 21 tangerines
  • Layer 7 - 28 tangerines
  • Layer 8 - 36 tangerines

Additionally, to know the total number of tangerines in the pyramid we must add the total number of tangerines in each layer as shown below:

  • 36 + 28 + 21 + 15 + 10 + 6 + 3 + 1 = 120

So the total tangerines are 120.

Note: This question is incomplete because the question is missing. Here is the complete question:

  1. How many mandarins are in a stack eight layers high?

Learn more about triangles in: https://brainly.com/question/2269348

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