Question

PLS HELP

What is the perimeter of the rhombus below?


A.
`8√(5)`

B.
`5√(8)`

C.
`4√(5)`

D.
`5√(4)`

Answer 1

8√5 units.

Explanation:

See the diagram in the coordinate plane attached.

A rhombus has four equal sides and to find the perimeter of the rhombus we have to measure any of the sides of the figure of the rhombus.

The coordinates of the topmost point are (-1,-1) and that of the rightmost point are (3,-3).

Therefore, side length of the rhombus will be

`\sqrt{(- 1 - 3)^(2) + (- 1 - (- 3))^(2)} = √(20) = 2√(5)` units.

So, the perimeter of the rhombus will be (4 × 2√5) units = 8√5 units. (Answer)

The distance between two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` on a coordinate plane is given by

`\sqrt{(x_(1) - x_(2))^(2) + (y_(1) - y_(2))^(2)}`