-If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28.

Question

Quizplus · Accepted Answer

The diagonals of a rhombus bisect each other at right angles. Using the Pythagorean theorem on one of the right-angled triangles formed by the diagonals, the length of each side of the rhombus is √((6/2)^2 + (8/2)^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5. Since a rhombus has four equal sides, the perimeter is 4 times the length of one side, which is 4*5 = 20, not 28.

-If the Diagonals of a Rhombus Have Lengths 6 and 8