Question

which set is a Pythagoral triplet (1) (5,12,13) (2) (8,15,17) (3) (10,15,25) (4) none
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Answer 1

Answer:

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is equivalent to finding positive integers a, b, and c satisfying

a^2+b^2=c^2.  

(1)

The smallest and best-known Pythagorean triple is (a,b,c)=(3,4,5). The right triangle having these side lengths is sometimes called the 3, 4, 5 triangle.

PythagoreanTriples

Plots of points in the (a,b)-plane such that (a,b,sqrt(a^2+b^2)) is a Pythagorean triple are shown above for successively larger bounds. These plots include negative values of a and b, and are therefore symmetric about both the x- and y-axes.

PythagoreanTriplesAC

Similarly, plots of points in the (a,c)-plane such that (a,sqrt(c^2-a^2),c) is a Pythagorean triple are shown above for successively larger bounds.

PrimitivePythagoreanTriple

It is usual to consider only primitive Pythagorean triples (also called "reduced"triples) in which a and b are relatively prime, since other solutions can be generated trivially from the primitive ones. The primitive triples are illustrated above, and it can be seen immediately that the radial lines corresponding to imprimitive triples in the original plot are absent in this figure. For primitive solutions, one of a or b must be even, and the other odd (Shanks 1993, p. 141), with c always odd.

In addition, one side of every Pythagorean triple is divisible by 3, another by 4, and another by 5. One side may have two of these divisors, as in (8, 15,

Step-by-step explanation: