The function that models the relationships among x, y, and r is [tex]r=\sqrt{x^2+y^2}[/tex]
"It is a triangle having one of the angle measures 90° "
"It is the longest side of the right triangle."
"For a right triangle,
[tex]a^2+b^2=c^2[/tex], where c is the hypotenuse of the right triangle and a, b are other two sides of right triangle."
For given question,
We need to write a function that models the relationships among x, y, and r.
Consider a right triangle ABC.
where AB = x, BC = y and hypotenuse AC = r
Using Pythagoras theorem,
[tex]x^{2} + y^{2} =r^{2}[/tex]
above function defines the relationships among x, y, and r.
Now we solve above equation for 'r',
[tex]\Rightarrow r^2=x^2+y^2\\\\\Rightarrow r=\sqrt{x^2+y^2}[/tex]
Therefore, the function that models the relationships among x, y, and r is [tex]r=\sqrt{x^2+y^2}[/tex]
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