If a right triangle has equal legs, it is by definition a 45-45-90 triangle. So, the two sides would be x and the hypotenuse would [tex] x\sqrt{2} [/tex]. However, we know the hypotenuse, and we do not see a [tex] \sqrt{2} [/tex] anywhere. That means it has already been multiplied by it, so to get the lengths of the sides we simply divide 26 by [tex] \sqrt{2} [/tex]. If you have to rationalize the denominator, the answer will be [tex] \frac{26}{\sqrt{2}} = \frac{26\sqrt{2}}{2} = 13\sqrt{2} [/tex]
[tex] \boxed {\text{pythagorean theorem :}a^2 + b^2 = c^2} [/tex]
Let the leg be x.
x² + x² = 26²
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Solve x:
x² + x² = 26²
Combine like terms:
2x² = 676
Divide both sides by 2:
x² = 338
Square root both sides:
x= √338
Put it in radical form:
x = 13√2
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Answer: 13√2
