Question

the perimeter of the figure below is 69.6ft find the length of the missing side. Side lengths: 8.3, 6.9, 6.9, 6.9, 6.9, 10.1, 2.3, 2.3, and 8.3

Answer 1

To find the length of the missing side, we first need to calculate the total length of the known sides and then subtract this total from the perimeter.

The known side lengths are:

- 8.3 ft
- 6.9 ft
- 6.9 ft
- 6.9 ft
- 6.9 ft
- 10.1 ft
- 2.3 ft
- 2.3 ft
- 8.3 ft

Now, we can calculate the sum of these lengths:

\[
8.3 + 6.9 + 6.9 + 6.9 + 6.9 + 10.1 + 2.3 + 2.3 + 8.3
\]

Calculating step by step:

\[
8.3 + 6.9 = 15.2
\]
\[
15.2 + 6.9 = 22.1
\]
\[
22.1 + 6.9 = 29.0
\]
\[
29.0 + 6.9 = 35.9
\]
\[
35.9 + 10.1 = 46.0
\]
\[
46.0 + 2.3 = 48.3
\]
\[
48.3 + 2.3 = 50.6
\]
\[
50.6 + 8.3 = 58.9
\]

So, the total length of the known sides is \(58.9\) ft.

Given that the perimeter of the figure is \(69.6\) ft, we can find the length of the missing side by subtracting the total length of the known sides from the perimeter:

\[
\text{Missing side} = \text{Perimeter} - \text{Total length of known sides}
\]
\[
\text{Missing side} = 69.6 - 58.9 = 10.7 \text{ ft}
\]

Thus, the length of the missing side is **10.7 ft**.