Question

Rhombus STAR has vertices S(–1,2), T(2,3), A(3,0), and R(0,–1).What is the perimeter of rhombus STAR?

Answer 1

Answer:

4√10

Step-by-step explanation:

Side of rhombus by distance formula =

$\sqrt{9 + 1 } = \sqrt{10}$

Perimeter = 4 × side = 4√10

Answer 2

The perimeter of the rhombus is 4√10 units.

Given:

For a rhombus STAR, the coordinates of its vertices are as follows;

S ≡ (-1, 2)

T ≡ (2, 3)

A ≡ (3, 0)

R ≡ (0, -1)

To Find:

The perimeter of the rhombus STAR =?

Solution:

We know the famous property of rhombus which states that all the sides of a rhombus are of equal lengths.

And, The perimeter of any polygon is the sum of the length of its sides.

i.e., For a rhombus, the perimeter is the value that is equal to four times the length of one of its sides.

Let, the side of rhombus STAR be 'a' units.

Now, here by using the distance formula to calculate the distance between two coordinates;

For (x, y) and (a, b)

The distance between the above coordinates is given by;

d = $\sqrt{(x-a)^{2} +(y-b)^{2} }$ units.

Now, for the given rhombus a will be equal to the distance between S ≡ (-1, 2) and T ≡ (2, 3)

i.e.,  a = $\sqrt{(-1-2)^{2}+(2-3)^{2} }$

∴   a = $\sqrt{(-3)^{2} +(-1)^{2} }$

∴   a = √10

And perimeter of the rhombus  = 4 × a

∴ perimeter of the rhombus   = 4√10

Therefore, The perimeter of the rhombus STAR is 4√10 units.

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