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The diagonals of a rhombus have lenghts 16 and 30. Find the perimeter of the rhombus.

  • math -

    The sides, which are equal since it is a rhombus, have a length dimension of sqrt (8^2 + 15^2) = sqrt(289) = 17, because the diagonals are perpendicular. The perimeter is therefore 4x17 = 68

  • math -

    why would you add (8^2 + 15^2)

  • math -

    I am applying the Pythagorean theorem
    a^2 + b^2 = c^2
    c is the length of a side
    a and b are half the lengths of the two diagonals. Draw yourself a picture with intersetinc diagonals and you will see the four congruent right triangles. Make sure you do it for a rhombus, which is a parallelogram with all sides equal.

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