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 possible length for one of the sides of isosceles triangle DEF?

Explain please? With the right formula and how you do it?

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  1. the right triangle is a 6-8-10 triangle, with perimeter 24.

    So, the isosceles triangle has two sides equal, and they must be less than 12 each.

    So, the greatest side of DEF must be less than 12, or 11. It has sides 11,11,2.

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  2. Thank you, but is there an equation that you can do this?

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  3. They tell you that the legs of the right triangle are 6 and 8. It is obvious that the height of the triangle would be the 6, and the length would be the 8. With the given numbers 6 and 8, you can tell that we are going to be increasing by 2, which is where we get the 10 from on the slanted side of the right triangle. The perimeter of the right triangle is 24. We know this because we added all of the sides together. Half of 24 is 12, so we know that the isosceles triangle has to be less than 12. Two of the sides of the isosceles triangle have to be the same, and that is why it would be 11, 11, 2.

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  4. continuation from the above paragraph. If you add 11, 11, and 2 together, you get 24, which was the perimeter of the right triangle also. This is how you know you have gotten the correct answer.

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  5. Which of the following correctly classifies the triangle?

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  6. What is the approximate perimeter of the quadrilateral?

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  7. 10. The vertices of a triangle are listed below.

    J(2,-7), K(2,5), L(10,-1)

    Which of the following correctly classifies the triangle?
    A. The triangle is an acute isosceles triangle.
    B. The triangle is an acute equilateral triangle.
    C. The triangle is a right isosceles triangle.
    D. The triangle is an acute scalene triangle.

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