Question

If a right triangle has equal legs, and the hypotenuse is 26 ft. how long is each leg (leave answer in radical form)

Answer 1

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 $x\sqrt{2}$. However, we know the hypotenuse, and we do not see a $\sqrt{2}$ anywhere. That means it has already been multiplied by it, so to get the lengths of the sides we simply divide 26 by $\sqrt{2}$. If you have to rationalize the denominator, the answer will be $\frac{26}{\sqrt{2}} = \frac{26\sqrt{2}}{2} = 13\sqrt{2}$

Answer 2

$\boxed {\text{pythagorean theorem :}a^2 + b^2 = c^2}$

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