Using the perimeter concept, it is found that the perimeter of the polygon is of 24.1 units.
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- The perimeter of a polygon is the sum of the lengths of all its sides.
- One side has length 1 unit.
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- The second side is the hypotenuse of a right triangle with sides of length 3 and 4, thus, applying the Pytagorean Theorem:
[tex]s^2 = 3^2 + 4^2[/tex]
[tex]s^2 = 9 + 16[/tex]
[tex]s^2 = 25[/tex]
[tex]s = 5[/tex]
- One of the sides has length of 5 units.
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- The third side is the hypotenuse of a right triangle of sides with lengths 5 and 7, thus:
[tex]s^2 = 5^2 + 7^2[/tex]
[tex]s^2 = 25 + 49[/tex]
[tex]s^2 = 74[/tex]
[tex]s = 8.6[/tex]
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- The final side is the hypotenuse of a right triangle with sides of lengths 3 and 9, thus:
[tex]s^2 = 3^2 + 9^2[/tex]
[tex]s^2 = 9 + 81[/tex]
[tex]s^2 = 90[/tex]
[tex]s = 9.5[/tex]
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- The lengths of the sides are: 1, 5, 8.6 and 9.5.
- Thus, the perimeter is of:
[tex]P = 1 + 5 + 8.6 + 9.5 = 24.1[/tex]
The perimeter of the polygon is of 24.1 units.
A similar problem is given at https://brainly.com/question/6139098
