Question

In the figure, \(\Delta A_{0}A_{1}A_{2}\) is an isosceles right-angled triangle with the hypotenuse \(A_{0}A_{1}\)=8cm. The second isosceles right-angled triangle \(\Delta A_{1}A_{2}A_{3}\) is generated by using the shorter side (\(A_{1}A_{2}\)) of \(\Delta A_{0}A_{1}A_{2}\) as the hypotenuse of the new triangle. The process is repeated infinitely.
(a) Find the lengths of \(A_{1}A_{2}\), \(A_{1}A_{3}\) and \(A_{3}A_{4}\).
(b) Find the total length of \(A_{0}A_{1}A_{2}A_{3}...A_{8}\).
(c) Find the total area of all the triangles formed.

Answer 1

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