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

The perimeter of a rhombus is the sum of its side lengths.

The perimeter of the rhombus is

The given parameters are:

The perimeter is calculated as:

So, we have:

Evaluate all exponents

Take the square root of x^2

Hence, the perimeter of the rhombus is

Read more about perimeters at:

link

10

step-by-step explanation:

7+3=10