Pythagorean theorem straightedge and compass. Pythagoras's theorem enables construction of incommensurable lengths because the hypotenuse of a triangle is related to the sides by the square root operation. The figure on the right shows how to construct line segments whose lengths are in the ratio of the square root of any positive integer. Each triangle has a side (labeled "1") that is the chosen unit for measurement. In each right triangle, Pythagoras's theorem establishes the length of the hypotenuse in terms of this unit. If a hypotenuse is related to the unit by the square root of a positive integer that is
Hypotenuse is the square root of 25, that is, 5. The word "hypotenuse" is derived from Greek (sc. or ), meaning "[side] subtending the right angle" (Apollodorus), The Greek term was loaned into Late Latin, as "hypotēnūsa". Adoption as a learned Latinism used in modern languages dates to the 16th century. The spelling in "-e", as "hypotenuse", is French in origin (Estienne de La Roche 1520). The length of the hypotenuse is calculated using the square root function implied by the Pythagorean theorem. Using the common notation that the length of the two legs of the triangle (the sides perpendicular to