What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 1 and 10?
1 Answer
Dec 25, 2015
Explanation:
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)#
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#
