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The lengths of the diagonals of a rhombus are 20 and 48 meters. What is the perimeter of the rhombus?
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In any rhombus, diagonals bisect each other and are perpendicular.
THEREFORE, the diagonals divide a rhombus into four congruent right-angled triangles.
Consider any of these triangle. Its legs are half-diagonals.
In our case, the legs of the considered triangle are 20/2 = 10 and 48/2 = 24 meters long.
Apply the Pythagorean theorem and calculate the hypotenuse length. It is
= = = 26 meters.
The hypotenuse is the side of the rhombus.
So, each side is 26 meters long.
Hence, the perimeter of the rhombus is 4*26 = 104 meters.
ANSWER. The perimeter of the rhombus is 4*26 = 104 meters.
