# If the hypotenuse of a 45°-45°-90° triangle has a length

If the hypotenuse of a 45°-45°-90° triangle has a length of $\surd 2$, how long are the legs?
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Velsenw
A 45°-45°-90° triangle is a right isosceles triangle. If x is the length of each leg, we can use the Pythagorean Theorem to write: ${x}^{2}+{x}^{2}={\left(\surd 2\right)}^{2}$
$2{x}^{2}=2$
${x}^{2}=1$
x=1