Answer:
The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.
Step-by-step explanation:
We shall use the Pythagorean Theorem to determine the length of the two oblique line of the figure. From Geometry, we know that the perimeter of the parallelogram is the sum of the lengths of the four sides of the parallelogram.
First, we calculate the length of the oblique line, that is:
[tex]l_{O} = \sqrt{5^{2} + 3^{2}}[/tex]
[tex]l_{O} = \sqrt{34}[/tex]
Second, we determine the length of the vertical line by direct observation, that is:
[tex]l_{V} = 12[/tex]
Lastly, the perimeter is determined by the following formula:
[tex]p = 2\cdot (l_{O}+l_{V})[/tex]
[tex]p = 24+2\sqrt{34}[/tex]
The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.
