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

  • geometry -

    The hypotenuse of the right triangle is sqrt(6^2 + 8^2) = 10.
    This makes the perimeter of RST 24.
    Therefore, the maximum integer side of triangle XYZ is (24 - 2)/2 = 11.

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