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the legs of an isosceles right triangle each measure 10 inches what is the length of the hypotenuse of this triangle to the nearest tenth of an inch

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Use the Pythagorean theorem:
[tex](\hbox{leg})^2+(\hbox{leg})^2=(\hbox{hypotenuse})^2 \\ 10^2+10^2=x^2 \\ 100+100=x^2 \\ x^2=200 \\ x=\sqrt{200} \\ x \approx 14.1[/tex]

The length of the hypotenuse is approximately 14.1 in.

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