A right triangle has legs $a$ and $b$ and hypotenuse $c.$  Find the largest possible value of
\[\frac{a + b}{c}.\]
Question:
A right triangle has legs $a$ and $b$ and hypotenuse $c.$  Find the largest possible value of
\[\frac{a + b}{c}.\]
Answer:
Let's think step by step.

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\sqrt{2}
A right triangle has legs $a$ and $b$ and hypotenuse $c.$  Find the largest possible value of
\[\frac{a + b}{c}.\]
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