Finding the area?

Geometry Level 3

The spiral of Theodorus (also called Pythagorean spiral) is composed of contiguous right triangles.

Which triangle has an area of 10 ? 10 ?

400th 100th 300th 200th 500th

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Feb 10, 2018

Notice the leg of the second triangle is 2 \sqrt{2} by using Pythagorean theorem

The leg of the third triangle is 3 \sqrt{3}

The leg of the fourth triangle is 2 and so on ...

Thus, the leg of triangle 400 is 400 = 20 ⟹ \sqrt{400}=20\implies the area is 20 × 1 2 = 10 \frac{20\times 1}{2}=10

2 Helpful 0 Interesting 0 Brilliant 0 Confused

The general area term computes to (1/2) * N^(1/2): N = natural number (FYI)!

tom engelsman - 2 years, 1 month ago

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Thanks, didn’t know that until now.

Hana Wehbi - 2 years, 1 month ago

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