Question 6 of 13intermediate🔧 ApplyNumerical4 marks

Find the perimeter of the shape at the nnth step of the sequence. Take the starting equilateral triangle to have a sidelength of 1 unit.

Correct Answer

Given: Starting equilateral triangle with side length 1 unit.

Step 1: Starting perimeter = 3×13 \times 1 = 3 units.

Step 2: At each step, each side of length L becomes 4 sides of length L/3.

Step 3: New length = 4 × (L/3) = 4L/3, which is 4/3 times the original.

Step 4: Perimeter gets multiplied by 4/3 at each step.

Step 5: Perimeter at step n = 3 × (4/3)^n units.

Verification: At Step 0: 3 units At Step 1: 4 units At Step 2: 16/3 units

Answer: Perimeter at step n = 3 × (4/3)^n units. The perimeter increases without bound as n increases.

Exercise: Figure it Out (Section 2) | Q: 3 | (Page Page 4)
For More Understanding

Explanation

The chapter describes how each side of length L is replaced by 4 sides of length L/3 each, giving total length 4L/3. So the perimeter is multiplied by 4/3 at each step. Starting with perimeter 3, after n steps the perimeter is 3 × (4/3)^n.

Solution Steps

  1. Step 1: Starting perimeter = 3×13 \times 1 = 3 units.

  2. Step 2: At each step, each side of length L becomes 4 sides of length L/3.

  3. Step 3: New length = 4 × (L/3) = 4L/3, which is 4/3 times the original.

  4. Step 4: Perimeter gets multiplied by 4/3 at each step.

  5. Step 5: Perimeter at step n = 3 × (4/3)^n units.

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