Question

What is the difference in perimeters of the ${17}^{\text{th}}and{16}^{\text{th}}$ triangles in the Spiral of Theodorus?

• A. 0.2436 units
• B. 0.4426 units
• C. 0.2426 units
• D. 0.3426 units

Answer 1

The correct option is C

0.2426 units

General formula:

Perimeter of n${}^{\text{th}}$ triangle - Perimeter of (n-1)${}^{\text{th}}$ triangle = $\sqrt{n+1}-\sqrt{n-1}$

Put n=17

$\Rightarrow$ Perimeter of 17${}^{\text{th}}$ triangle - Perimeter of (17-1)${}^{\text{th}}$ triangle = $\sqrt{17+1}-\sqrt{17-1}$

$\Rightarrow \sqrt{18}-\sqrt{16}$

$\Rightarrow 4.2426-4$

$\Rightarrow 0.2426\text{units}$