Question

What is the perimeter of rhombus WXYZ?

units
12 units
units
20 units

Answer 1

Let O be the intersection of the vertical line through ZX, and the horizontal line through YW.

The coordinates of this point are clearly (5, 2) as it is at the same x-coordinate as X and Z, and y-coordinate as Y and W.


So, YZO is a right triangle. By the Pythagorean theorem:


`ZY= \sqrt{{YO}^2+{OZ}^2}= √(2^2+3^2)= √(4+9)= √(13)`.


Since all sides of a rhombus are equal, then the perimeter is :


`P(XWZY)=4 √(13)` units.


Answer: third choice.