What is the length of the missing side of a polygon with a perimeter of 56 cm where three sides measure 9 cm each and two sides measure 8 cm each?

To determine the length of the missing side of the polygon, we begin by calculating the total length contributed by the known sides. The polygon has three sides measuring 9 cm each and two sides measuring 8 cm each.

First, we calculate the total length of the three sides measuring 9 cm:

[

3 \times 9 = 27 \text{ cm}

]

Next, we calculate the total length of the two sides measuring 8 cm:

[

2 \times 8 = 16 \text{ cm}

]

Now, we add these two contributions to find the total length of the known sides:

[

27 \text{ cm} + 16 \text{ cm} = 43 \text{ cm}

]

The perimeter of the polygon is given as 56 cm. To find the length of the missing side, we subtract the total length of the known sides from the perimeter:

[

56 \text{ cm} - 43 \text{ cm} = 13 \text{ cm}

]

Thus, the length of the missing side is 13 cm, which aligns with the first option. This calculation confirms that the answer is indeed true, as it completes the total perimeter