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The perimeter of a right triangle $RST$ is equal to the perimeter of isoceles triangle $xyz$ The lengths of the legs of the right triangle are 6 and 8. If the length of each side of the isoceles triangle is an integer what is the greatest possible length for one of the sides of isoceles triangle $xyz$?

The hypotenuse of $RST$ is $\sqrt{100} = 10$

For $xyz$ let $xy = yz$ as the two equal legs, and $zx$ is the unequal, the "base" side.

Perimeter of $RST$ = $xyz$ = $24$

So leg $zx = 2$ is the lowest length the triangle can have, so that the other two are integers.

$xy + yz = 22 = 2xy \implies xy = 11 = yz$

Is this correct?

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Yes. Correct answer, correct reasoning.

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  • $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. $\endgroup$ – Shaun Oct 6 '14 at 9:38
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    $\begingroup$ @Shaun Which part of "Is this correct?" did I fail to answer? $\endgroup$ – almagest Oct 6 '14 at 10:03
  • $\begingroup$ That was an automated reply; yes, it's an inappropriate one. I'm sorry. This answer was flagged as low quality due to its length. I agreed somewhat in my review, thinking that it'd be better off as a comment. Never mind :) $\endgroup$ – Shaun Oct 6 '14 at 10:16

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