Question

We have seen how we can draw a series of right triangles as in the picture.
How much more is the perimeter of the tenth triangle then the perimeter of the ninth triangle?

Answer 1

tenth $△=[\sqrt{10}+1+\sqrt{10+1}]$

$9^{th}△=\sqrt{9}+1+\sqrt{10}$

${10}^{th}-9^{th}$

$\Rightarrow (\sqrt{10}+1+\sqrt{11})-(3+1+\sqrt{10})$

$\Rightarrow \sqrt{11}-3$