What is the perimeter of a rhombus with diagonals of lengths 12 and 16 units?
A rhombus is a quadrilateral with four congruent sides, so I need to find the length of one side. I also know that the diagonals of a rhombus are perpendicular bisectors of each other, so they form four right triangles inside the rhombus. I can use the Pythagorean theorem to find the length of one side, since it is the hypotenuse of a right triangle with legs of half the lengths of the diagonals. So, the length of one side is sqrt((12/2)^2 + (16/2)^2) = sqrt(36 + 64) = sqrt(100) = 10 units. The perimeter of the rhombus is the sum of the lengths of the four sides, so it is 4 * 10 = 40 units. 