# If the two legs of an isosceles right triangle measure 7 inches, what is the length of its hypotenuse ?

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Ben G. Share
Mar 8, 2018

Using the Pythagorean Equation, you find the length to be $7 \sqrt{2}$

#### Explanation:

The Pythagorean Equation is only applicable to right triangles, which is what we have, luckily. The equation states that the square of the hypotenuse is equal to the sum of the squares of the sides.

Using this equation: ${a}^{2} + {b}^{2} = {c}^{2}$, you can plug in the two leg lengths to get the hypotenuse.

${7}^{2} + {7}^{2} = {c}^{2}$

$2 \cdot {7}^{2} = {c}^{2}$

$\sqrt{2 \cdot {7}^{2}} = c$

$c = 7 \cdot \sqrt{2}$

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