Hi, I have this homework which includes the picture I attached.image.jpg. The figure is made in a way the the hypothenuse of the previous triangle is the long side of the next one. The text (it’s in french), says that the area of any of those right triangle ‘‘n’’ is: A(n)= 6(5/4)^(2n-2). It also said that the side lenghts of the first right triangle were 3,4 and 5. The question only asked to find the area of a 7th triangle, which wasn’t too hard, but I wondered if it was possible to come up with a formula for the hypothenuse of any triangle ‘‘n’’.

I tried without much success or progress but I was just curious.

Thanks,

Thomas

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