Question

Use the Pythagorean Identity with x = 8 and y = 5 to generate a Pythagorean triple. is it A,B,C,D?a) 25, 64, 17b) 39, 80, 89c) 5, 12, 13d) 5, 8, 13

Answer 1

5 and 8 do not take part in any Pythagorean triple at the same time; therefore, we would identify the Pythagorean triple among the options.

In general, a Pythagorean triple is an arrangement of numbers (a,b,c), such that

`a^2+b^2=c^2`

Where a,b, and c are positive integers

Then, in our case,

a)

`17^2+25^2=914\\e4096=64^2`

b)

`39^2+80^2=7921=89^2`

c)

`5^2+12^2=169=13^2`

d)

`5^2+8^2=89\\e169=13^2`

Options b) and c) are Pythagorean triples.

Due to the lack of information about the 'Pythagorean identity' one is supposed to use, we cannot determine which of the two options is the correct one.

However, notice that

`\begin{gathered} 5+8=13 \\ \Rightarrow(5+8)^2+5^2=12^2 \end{gathered}`

Therefore, option c) might be a more suitable answer to the question.