What is the gcf of 45 and 60 using prime factorization?

45 = 3×3×5

60 = 2×2×3×5

Factors that are common to both products are 3×5.

3×5 = 15 is the GCF of 45 and 60

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