Question

What is the difference in perimeters of the $9^{th}and{8}^{th}$ triangles in the Spiral of Theodorus?

• A. 0.3335 units
• B. 0.4338 units
• C. 0.3338 units
• D. 0.3348 units

Answer 1

The correct option is C

0.3338 units

General formula:

$Perimeterof{n}^{th}triangle-Perimeterof(n-1{)}^{th}triangle=\sqrt{n+1}-\sqrt{n-1}$

Plug in n=9

$\Rightarrow Perimeterof{9}^{th}triangle-Perimeterof(9-1{)}^{th}triangle=\sqrt{9+1}-\sqrt{9-1}$

$\Rightarrow Perimeterof{9}^{th}triangle-Perimeterof{8}^{th}triangle=\sqrt{9+1}-\sqrt{9-1}$

$\Rightarrow \sqrt{10}-\sqrt{8}$

$\Rightarrow 3.1622-2.8284$

$\Rightarrow 0.3338units$