The two diagonals of a rhombus measure 24 cm and 10 cm. What is its perimeter in cm?

The diagonals of a rhombus bisect each other at right angles, so each side is the hypotenuse of a right triangle with legs 12 cm and 5 cm: side = √$(144+25)=13$ cm, and the perimeter = $4\times 13=52$ cm. The trap 120 is the AREA, $(1/2)\times 24\times 10=120$ sq cm, quoted as if it were a length; $68=2(24+10)$ treats the diagonals as the sides of a rectangle; 34 just adds the two diagonals.