the lengths of the diagonals of a rhombus are 2x and 8x. what expression gives the perimeter of the rhombus?

Expression gives the perimeter = 4x√17

Step-by-step explanation:

∵ The diagonals of the rhombus ⊥ to each other and

bisects each other

∴ Half the longest diagonal = 8x/2 = 4x

∴ Half the shortest diagonal = 2x/2 = x

Use Pythagoras theorem to find the length of the side of the rhombus

∴ The length of the side = √[ (4x) ² + (x) ²] = √[16x² + x²] = √ (17x²)

∴ S = x√17

∵ Perimeter of the rhombus = 4 * S

∴ P = 4 * x√17 = 4x√17