What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 1 and 10?

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Answer 1 · 2015-12-25T17:43:53

$\sqrt{101} \approx 10.05$ $sqrt(101) ~~ 10.05$

By Pythagoras Theorem, the length of the hypotenuse is the square root of the sum of the squares of the lengths of the two other sides.

$\sqrt{1^{2} + 10^{2}} = \sqrt{1 + 100} = \sqrt{101}$ $sqrt(1^2+10^2) = sqrt(1+100) = sqrt(101)$

This is an irrational number, with no terminating or repeating decimal expansion, but it can be represented as a continued fraction:

$sqrt(101) = [10;bar(20)] = 10+1/(20+1/(20+1/(20+1/(20+...))))$

If you terminate the continued fraction early then you get a rational approximation.

For example:

$sqrt(101) ~~ [10;20] = 10+1/20 = 10.05$