19In a right triangleABC, the legs areAB= 5 andBC= 12, and in the right triangleDEF, the hypotenuse isDE= 10, andEF= 8. Which isDF+AC?

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- Jun 24th 2007, 11:01 PMsanee66hypotenuse help please19
**In a right triangle***ABC*, the legs are*AB*= 5 and*BC*= 12, and in the right triangle*DEF*, the hypotenuse is*DE*= 10, and*EF*= 8. Which is*DF*+*AC*?

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- Jun 24th 2007, 11:11 PMCaptainBlack
In a right triangle the "legs" are the sides other than the hypotenuse, so in

$\displaystyle \triangle ABC$ (by Pythagoras' theorem) $\displaystyle AC=\sqrt{5^2+12^2} = 13$.

In $\displaystyle \triangle D E F$ we have the hypotenuse $\displaystyle DE$ is $\displaystyle 10$, and leg $\displaystyle EF=8$, so:

$\displaystyle

DE^2 = EF^2+DF^2,

$

so:

$\displaystyle

DF=\sqrt{10^2-8^2}=6.

$

RonL