Question

Can anybody help me on this

Answer 1

Answer:

The correct answer is third option 4√13

Step-by-step explanation:

It is given that two consecutive vertices of rhombus are (2, 5) and (-1, 3)

To find the side of rhombus

Side = √[(-1 -2)² + ( 5 - 3)²]

  = √[(-3)² + 2²] =  √(9 + 4) =  √13

To find the perimeter

Perimeter = 4 * side

  = 4 *  √13 = 4 √13

Answer 2

Hello!

The answer is:

$4\sqrt{13}$

Why?

To solve this problem, we need to remember the formula to calculate the perimeter of a rhombus.

$P=side+side+side+side=4s$

Now, to calculate the the perimeter, we just need to know the length of one side of the rhombus, we can find the lenght of one side of the rhombus using the given information since two points are given and we know that both points represents two consecutives vertices of the rhombus. Finding the distance between these two consecutives vertices (points) we will know the length of one side of the rhombus.

We can calculate the distance between two points, using the following formula:

$d=\sqrt{(x_{2}-x_{1})^{2} +{(y_{2}-y_{1})^{2}}$

We are given two points:

$(2,5)\\(-1,3)$

Where,

$x_{2}=-1\\y_{2}=3\\x_{1}=2\\y_{1}=5$

Now, substituting we have:

$d=\sqrt{(-1-2)^{2}+{(3-5)^{2}}$

$d=\sqrt{(-3)^{2}+{(-2)^{2}}$

$d=\sqrt{(9+4)}=\sqrt{13}$

Now, that we know the distance of one of the sides of the rhombus, the perimeter is equal to:

$p=4(\sqrt{10})=4\sqrt{13}$

So, the answer is the second option $P=4\sqrt{13}$

Have a nice day!