# geometry

posted by .

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.

## Similar Questions

1. ### isosceles triangle

An isosceles triangle is a triangle that has two equal sides. Find AB, BC and AC. Determine if the triangle is isoseles or not based on the lengths of the three sides. can someone show me how to solve?
2. ### algebra

The base of an isosceles triangle and one of its legs have lengths that have consecutive integers. The leg is longer than the base. The perimeter of the triangle is 20. Find the length of each side of the triangle. *Please help me- …
3. ### geometry

The perimeter of an isosceles triangle is 42 cm . its base is 2/3 times the sum of the equal sides . find the length of each side and the area of the triangle.
4. ### Math (Geometry)

The perimeter of right triangle ABC is equal to the perimeter of isosceles triangle DEF. 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 …
5. ### Math

If all of the following triangles have the same perimeter, which has the greater area?
6. ### math

The base of an isosceles triangle is four less than the sum of the lengths of the legs. If the perimeter of the triangle is 44, find the length of the three sides of the triangle.[ Only an algebraic solution will be accepted ]