Answer:
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
