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Are the diagonals of a rhombus ALWAYS less than the perimeter of the rhombus?

2006-12-12 15:43:42 · 1 answers · asked by Muffins 1 in Education & Reference Homework Help

1 answers

Yes; the diagonals divide the rhombus into four congruent right triangles. The sides of the rhombus are the hypotenuses of the triangles and each half of each diagonal is a side of one of these right triangles. Since the hypotenuse of a right triangle is its longest side, then the sum of four hypotenuses, which is also the perimeter of the rhombus, is greater than the sum of the four sides, which is also the sum of the diagonals of the rhombus.

2006-12-12 16:04:03 · answer #1 · answered by wild_turkey_willie 5 · 0 0

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